Question

At what value(s) of x does f(x) = x^3 - 3x^2 - 24x have a relative minimum?

Answer 1

@phi

Answer 2

@satellite73

Answer 3

f'(x) = 3x^2 + 6x + 24
f''(x) = 6x + 6
Solve f'(x) for 0, quadratic equation, place the two solution in f''(x) if the values are positive they are a relative minimum.

Answer 4

what if i do the first derivative test

Answer 5

or second derivative test

Answer 6

What KenLJW is saying is that the first derivative can be used to find the critical points, or points that are either maximums or minimums. You use the second derivative to tell if the graph is accelerating upwards or downwards. If it is going upwards, you can imagine a sort of valley-type shape, so it would be a minimum. If it is going downwards, then you have a maximum, because it is shaped like a mountain. Just do what Ken said and you should have your answer.

Answer 7

ok thx :)