Answer:
D; [tex]f'(0.4)<f'(-1.5)<f'(-3.1)[/tex]
Step-by-step explanation:
First, we need to differentiate the function. This gives us the derivative:
[tex]f'(x)=x^{6}+3x^{5}-5x^{4}-15x^{3}+4x^{2}+12x[/tex]
Now, we just need to plug in the x-values of -3.1, -1.5, and 0.4
[tex]f'(-3.1)=14.974\\f'(-1.5)=4.922\\f'(0.4)=4.387[/tex]
Looking at these values, we can see that
[tex]f'(0.4)<f'(-1.5)<f'(-3.1)[/tex]
This means that D is the answer.
