Find the derivative of f 0f x.

f(x) = x^2 - 8x - 17 at x = 4

First you try it

Use the general idea that
d/dx x^n = n x^(n-1)

for example

d/dx x^16 = 16 x^15

to evaluate that at x = 1
16 1^15 = 16

I am trying to say try to do it yourself first. That is the rule for differentiating powers of x.

To find the derivative of f(x), we can use the power rule, which states that for a function f(x) = x^n, the derivative is f'(x) = n*x^(n-1).

In this case, f(x) = x^2 - 8x - 17. We need to find f'(x) at x = 4.

Step 1: Find the derivative of f(x).
Using the power rule, we differentiate each term of the function separately:
- The derivative of x^2 is (2)x^(2-1) = 2x.
- The derivative of -8x is (-8)*(1)x^(1-1) = -8.
- The derivative of -17 is 0 (since a constant has a derivative of 0).

Therefore, f'(x) = 2x - 8.

Step 2: Evaluate f'(x) at x = 4.
Substitute x = 4 into the derivative expression f'(x) = 2x - 8:
f'(4) = 2(4) - 8 = 8 - 8 = 0.

Therefore, the derivative of f(x) = x^2 - 8x - 17 at x = 4 is 0.