Question

let f(x)=2x^2 - 4x + 8. a. find the values of x for which the slope of the curve y = f(x) is 0. b. find the values of x for which the slope of the curve y = f(x) is - 16. a. the slope of the curve is 0 at x = . (simplify your answer. use a comma to separate answers as needed.) b. the slope of the curve is - 16 at x = . (simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Find the derivative of f(x)

The derivative of $f(x)=2x^{2}-4x + 8$ using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$ is $f'(x)=4x-4$.

Step2: Solve for x when slope is 0

Set $f'(x)=0$. So, $4x - 4=0$. Add 4 to both sides: $4x=4$. Divide both sides by 4, we get $x = 1$.

Step3: Solve for x when slope is - 16

Set $f'(x)=-16$. So, $4x - 4=-16$. Add 4 to both sides: $4x=-12$. Divide both sides by 4, we get $x=-3$.

Answer:

a. 1
b. - 3