Question

(AP Calc) Let f be the function given by f(x)=....

Answer 1

D;
`f'(0.4)<f'(-1.5)<f'(-3.1)`

Explanation:

First, we need to differentiate the function. This gives us the derivative:

`f'(x)=x^(6)+3x^(5)-5x^(4)-15x^(3)+4x^(2)+12x`

Now, we just need to plug in the x-values of -3.1, -1.5, and 0.4

`f'(-3.1)=14.974\\f'(-1.5)=4.922\\f'(0.4)=4.387`

Looking at these values, we can see that

`f'(0.4)<f'(-1.5)<f'(-3.1)`

This means that D is the answer.