Find the derivative of f 0f x.
f(x) = x^2 - 8x - 17 at x = 4
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.
Thanks looks like I forgot to subtract 8
To find the derivative of f(x), we can apply the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) with respect to x is f'(x) = n*x^(n-1).
Given that f(x) = x^2 - 8x - 17, we can find the derivative of f(x) by applying the power rule to each term separately.
The derivative of x^2 is 2x^1, which simplifies to 2x.
The derivative of -8x is -8.
The derivative of -17 is 0, since -17 is a constant.
Now, we can add up the derivatives of each term to find the derivative of f(x):
f'(x) = 2x - 8 + 0
= 2x - 8
To evaluate the derivative at x = 4, we substitute x = 4 into the expression for the derivative:
f'(4) = 2(4) - 8
= 8 - 8
= 0
Therefore, the derivative of f(x) = x^2 - 8x - 17 at x = 4 is 0.
f(x) = x^2 - 8x - 17 at x = 4
I came up with 8 ?
f'(x) = 2 x -8
when x = 4
f'(x) = 2*4 - 8
= 0