# Calculus

Find the derivative of f 0f x.

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

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

I came up with 8 ?

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

when x = 4

f'(x) = 2*4 - 8
= 0

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3. You were given:

Find the derivative of f 0f x.

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

We first find the derivative of the given function and then replace x with 4 in the derivative we will find.

I will use the power rule to find the derivative of your function.

The Power Rule: The derivative of the term a(x^n) (with respect to x), where a and n are real numbers is:
(a times n)[x^ (n - 1)].

We apply the power rule on each term of the function individually.

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

The derivative of x^2 = 2x.

The derivative of 8x = 8

The derivative of any constant = 0.

So, the derivative of constant -17 = 0.

We now have the function:

f'(x) = 2x - 8

We now replace x with 4 and simplify.

f'(x) = 2(4) - 8

f'(x) = 8 - 8

f'(x) = 0

So, the derivative of the original function at x = 4 is ZERO.

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4. Thanks looks like I forgot to subtract 8

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