Question

CALCULUS HELP!!!!!?

Find the slope of the graph using the derivative…

f(x)=3(5-x)^2 (5,0)

PLEASE HELP...

Answer 1

Do you know how to find the derivative? c: It involves the power rule and the chain rule.

Answer 2

HONESTLY THATS WHAT IM HAVING TROUBLE WITH

Answer 3

Do you have to use the definition of the derivative, or can we go straight to derivatives of polynomials with positive integer exponents?

Answer 4

WELL, IT JUST ASKS TO FIND THE SLOPE OF THE GRAPH OF THE FUNCTION AT THE GIVEN POINT.

Answer 5

@zepdrix , I'll wait for you since you were first.

Answer 6

LOL! No no no C: go ahead, You're in good hands with Carol.
I need to go anyway ^^/

Answer 7

OK, zep was definitely right with suggesting the chain rule. That will take precedence. And with the chain rule, you work from the "outside" toward the "inside". I'll show you what I mean. Instead of 5-x, you can think of the function as 3u^2. You get the derivative of THAT first, and then work toward the inside by multiplying that by the derivative of 5-x (which is that u). So, the exponent first, and then what's "inside".

Answer 8

So, if we just look at 3u^2 for the time being, can you get the derivative of that first?

Answer 9

Hint: you lower the exponent by one and use the old exponent as an additional factor. So, if y= ax^b, then the derivative is bax^(b-1). With me so far?

Answer 10

SOOO 3x^2-1
=3x

Answer 11

Well, 2 mistakes, 1) be careful to write 3x^(2-1) . Otherwise the 1 would not be part of the exponent since exponentiation is prioritized over subtraction. The parentheses becomes absolutely required, not just suggested. 2) You have to put the factor of "2" in front.

Answer 12

So the derivative of 3u^2 is (2)(3)u^(2-1) = 6u

Answer 13

Next, by using the chain rule, you multiply the 6u by the derivative of what u is. u is 5-x, so the derivative of u is -1. Next you take that -1 and multiply it by 6u to get -6u. Last, substitute 5-x back into the u, and simplify if it is required. These are big clues, so try this and see what you get for an answer. Helps if you show asome work so if you get stuck, I'll know where to help you.

Answer 14

Stuck?

Answer 15

yes