Question

Let f"(x)=3x^3+2x-2 and f(x) have critical numbers -2,0, and 1. Determine if any of the critical numbers gives a relative minimun using the second derivative test.

Answer 1

the relative minimum ocuurs when the second derivative yields a positive value and it is at 1

Answer 2

thank you

Answer 3

Can you help me with one more please?

Answer 4

yes ofcourse

Answer 5

Let f be a twice-differentiable function whose derivative, f'(x), is decreasing for all x. Which of the folowing must be true for all x?

I. f(x)<0
II.f'(x)<0
III.f"(x)<0

Answer 6

iii f''x<0

Answer 7

slope of the graph of the second derivative must be less than zero for it to decrease for all values of x

Answer 8

So is it only at f"(x)<0 or can it be f"(x)<0 and f'(x)<0

Answer 9

given only f'x is decresing for all values of x ,doesn't mean f(x) is decresing

Answer 10

okay thanks