Question

Find the slope of the tangent line to the graph of f at the given point.

f(x) = x^2 + 5x at (4, 36)

A. 13

B. 21

C. 9

D. 3

Answer 1

i am going to hazard a guess that you do not yet know the simple rules for finding a derivative, and have to do this by hand

Answer 2

differentiate it
f'(x)=2x+5
now use x=4
f'(x)=2(4)+5
f'(x)=8+5y=13
f'(x)=m=13

Answer 3

let me know if i am right
if you know how to find derivatives quickly, you can just about do it in your head
if not, there is a bunch of work to do

Answer 4

no i havent really grasped the concept yet and @saadi its x^2 not 2x

Answer 5

@satellite73

Answer 6

i assume then finding the derivative from the first principle?

Answer 7

yes

Answer 8

you want \[\lim_{x\to 4}\frac{x^2+5x-36}{x-4}\]

Answer 9

you cannot of course replace \(x\) by 4 at this step, because you will get \(\frac{0}{0}\) so the gimmick is to factor, cancel, and then replace \(x\) by 4

Answer 10

and you know it MUST factor in the numerator, because if you replace \(x\) by 4 you get 0, therefore the numerator must factor as \((x-4)(\text{something})\)

Answer 11

you good from there?

Answer 12

what happens next?