Question

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

Answer 1

Answer:

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

Step-by-step 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.