| Author | Message | ||
     Xb9er |
I have a homework question as follows: Find an equation of the tangent line to the curve at the following point: y=(1-9x)^10 , (0,1) So how do I go about this? Thanks, chris | ||
| Hootowl |
This answer comes to you through 25 years of cobwebs; It's asking you what the slope (the line tangent to the point on the curve) is at that point. Find the prime derivative. | ||
| Xb9er |
Derivative is the slope of the tangent line. | ||
| Reindog |
It's been 34 years for me. Use the chain rule: y'=10(1-9x)^9 * (-9)=-90(1-9x)^9 The equation for the tangent line at x=0: y=-90(1-9*0)^9 = -90. y=-90 is the answer. | ||
| Reindog |
Let me know if I Passed or Failed. I barely remember this stuff. | ||
| Hootowl |
The prime derivative will give you an equation for the slope of the tangent at any point on the curve. Evaluate the prime derivative for the coordinate given, and that is the equation that defines the line. | ||
| Panhead_dan |
Before you can evaluate the prime derivative, you must first invent the universe. | ||
| Fast1075 |
Jed: Whaddya lern in school today Jethro? (Proudly) Why uncle Jed I lernt naught plus naught equals naught.  | ||
| Brumbear |
my son is in 8th grade and just started calc I'll see what he comes up with me I dunno | ||
| Hootowl |
Calculus in 8th grade. Impressive. | ||
| Xb9er |
-90 is not the answer according to webwork. I know I need to start off using the difference quotient: (x+h)-f(x)/h and then start using the chain rule. this class is going to be the death of me. I'm a marketing and management major, why derivatives?! Brumbear, your son must be a genius, reward him with Buell of his choice. | ||
| Blake |
Reindog almost got it; he solved for the slope, but is impatient in his codgerliness (Obama may be to blame). He just needs the equation for a y-intercept of 1. y = -90x + 1 | ||
| Reindog |
Would you believe? y=-90x+1 | ||
| Reindog |
Cool, I didn't see you post, Blake, and came up with the same equation. | ||
| Blake |
d/dx (1-9x)10 = 10(1-9x)9(-9). Just like Reindog noted. Solve that derivative for x=0 then gives slope of tangent line at that point, which works out to -90 as Reindog showed. The y-intercept is conveniently given as the point of interest, y=1.0, so the equation for the line passing through (0,1) and tangent to the curve there is... y = -90x +1 Economic theory makes great use of calculus. Almost anything that is usefully graphed/plotted can make great use of calculus for theoretical modeling or even just historical analysis. Embrace the calculus. (Message edited by blake on September 29, 2014) | ||
| Reindog |
xb9er, Try and find a way to enjoy calculus as it is a perfect expression of logical thinking and it is a foundation into understanding how things change. It is a monument to beauty. | ||
| Blake |
Hah. Tom, you did the hard work. I thought the chain rule was to check oil and adjust it at every oil change. | ||
| Xb9er |
-90x+1 is the answer! Thanks fellas. Just another reason why I love the badweb! Reindog, how did you remember the chain rule after 34 years? Teach me your ways. Blake, why am I not surprised you knew how to derive this?hahahaha | ||
| Aesquire |
Darn. I was still digging out my slide rule. | ||
| Reindog |
I first broke out in a cold sweat when you first formulated the problem but it just came back in steps. Thanks, it was fun. Not knowing my future while I was headed to being a lifelong Teamster truck loader, I took a calculus course out of the blue for a year. It was intimidating because I had not studied math in seven years. After calculus, it was a year of differential equations. After differential equations, it was a year of Mathematical Physics. That will make your head spin. I now am a design engineer of integrated circuits with a Masters Degree in EE. Stick with your studies because you will achieve more than you can dream. Stay with it because you will see the beauty of the differential and integral calculus. It is mind boggling that it was there all along and it took Man to discover it. The secret? If you haven't done so already, have a talk with yourself that you will persevere no matter how difficult the subject. It is overwhelming at times but make a contract with yourself that you will NOT give up. Good luck with your studies as I am envious of you. Chris, I just read your profile page after writing all this high faluting stuff. You already know lots more than what I can tell you. Thanks for your service, dude. (Message edited by reindog on September 29, 2014) | ||
| Xb9er |
I started school 7 years after high school. Let me tell you, 6 years as an Infantryman, you really don't give math much of a thought lol. Thanks for your help. This is my last math course. | ||
| Brumbear |
Well the boy got it wrong but I am proud of him for trying!!! I can't even understand any of it!!!! i will post his work maybe somebody can help me understand what he did and what he did wrong!!!  | ||
| Blake |
Geez, poor kid! He's just not yet got to the chain rule for figuring derivatives, f'(x) as he designates it. f'(h+kx)n = n(h+kx)(n-1) * f'(h+kx) f'(h+kx)n = n(h+kx)(n-1) * k He got the y-intercept part right. (Message edited by blake on September 30, 2014) | ||
| Blake |
That's a college Calc 1 problem by the way! What math will he be learning by senior year? Linear algebra, statistics? Highly recommend both. He'll be just two course shy of a math minor! (Message edited by blake on September 30, 2014) | ||
| Etennuly |
 I did this stuff in college as a Business Administration student. It gave me headaches. I aced the two courses I needed to take, but never understood the principals behind the actual use for factoring and such. I felt like they were showing me how to build a great big machine, then parking it and not telling me what it was for. The answer I alway got was you are finding a point on a line in a graph. I understand that it goes three dimensional at some point, to find those points in space, but not one time in twenty two years of being in business have I needed, or used any of those calculations. The one formula I did need I had to figure out from scratch, on my own, because when I asked some math whiz and accounting types they could not help me, and it could not be found at that time in books. I needed to know the formula for finding the cost of a good if I only had a total price that included tax and the tax rate. At the time many customers were asking for a quick off the top total estimate price for work to be done. So the total would be a nice round number like $1500. Then I had to back the tax out of it to get the actual cost. | ||
| Blake |
Vern, So true. Very rare are the math professors who go beyond the booklearning and make it real. Fortunately in engineering we are forced to make it real. Some guys remember beam equations, but it sure is nice to be able to derive them through integration. That said, I now have the app for that on my phone. | ||
| Etennuly |
I now have the app for that on my phone The newest smart folks don't need to know much or think anything, just how to look up apps. | ||
| 86129squids |
 I suck at abstract math. I excel at abstract thought. And movies. Watching them that is. "Pi" the movie, is good. Kohannisquatsi is also good watchin. Phillip Glass did the soundtrack, either you appreciate it, or you might defenestrate yourself. €€ what the hell is that?!?! Just mashed the keyboard. | ||
| Gregtonn |
I felt like they were showing me how to build a great big machine, then parking it and not telling me what it was for. Unfortunately math and all its cousins have been taught backasswards for years. It could be so much more interesting if you were given real world problems first and then shown how to apply math/calc/trig/geom/stats to solve them. Also tailoring problems toward students areas of interest always makes learning more effective and enjoyable. Anybody care to come up with some real world math problems concerning motorcycle performance? G | ||
| Reepicheep |
I needed calculus when building a closed loop heated grip controller for my Uly. | ||
| Pwnzor |
"Pi" the movie, is good.  | ||
| Strokizator |
I just hang around you guys and folks automatically think I'm smart too (as long as I keep my mouth shut). I'm a prime example of how far you can get in life by making people believe you know what you're talking about. | ||
| Etennuly |
Sometimes I feel like I move up two points on the IQ scale reading these kind of threads.....no worries though, there are plenty of other threads to keep the balance!  |
