Find the derivative of f(x) = 8×2 + 11x at x = 7.?

Question

I need help finding the derivative of the function f(x) = 8x² + 11x at the point x = 7. The answer choices are 123, -147, 156, and 189. I have reached the expression 8h + 8x - 11. What should I do next to find the correct derivative?

Anonymous · Accepted Answer

In order to find the derivative of f(x) = 8x² + 11x at x = 7, you need to first differentiate f(x) = 8x² + 11x, and after you’re done you’ll plug in 7, i.e. making use of Liebniz Notation: f(x) = x^n → f'(x) = nx^(n – 1) to differentiate f(x) = 8x² + 11x, then 
f'(x) = 2*8x^(2 – 1) + 1*11x^(1 – 1) 
f'(x) = 16x + 11, where x = 7, then by substitution you’ll have 
f'(x) = 16(7) + 11 
f'(x) = 112 + 11 
f'(x) = 123 …Ans.

Elissa O&#039;Keefe V · Answer

f(x) = 8x^2 + 11x
f ‘(x) = 16x + 11  [@ x = 7]
f ‘(x) = 123
euclid
I have gotten to this point: 8h+8x-11.Now what?
Additional Details
So I see that you got an answer but how’d you get the 16x?
the real question is:  how did you get (8h + 8x – 11) ??
lim [f(x + h) – f(x)]/h
h->0
{[8(x + h)^2 + 11(x + h)] – [8x^2 + 11x]}/h=
 {[8(x^2 + 2xh + h^2) + 11x + 11h] – (8x^2 + 11x)}/h =
(8x^2 + 16xh + 8h^2 + 11x + 11h – 8x^2 – 11x)/h =
(16xh + 8h^2 + 11h)/h
lim [h(16x + 8h + 11)/h] = 16x + 11
x->0
that is where 16x + 11 comes from…show your work !

Anonymous · Answer

That’s not right.
the result should be f ‘ ( x ) = 16x + 11 
f ‘ ( 7 ) = 16( 7 ) + 11 
f ‘ ( 7 ) = 123

Anonymous

Find the derivative of f(x) = 8×2 + 11x at x = 7.?

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