Question

examine the graph of f(x)=10x^3+3x^2-12x what are the intervals on which the rate of change of the function will be positive

My teacher has not been helping me and I do not understand this question at all any tips will be greatly appreciated

Answer 1

If this is not a calculus class, then about all you can do is look at the graph. You will notice that it has a maximum at about (-0.74,6.47) and a minimum at about (0.54,-4.03).
So, f(x) is decreasing (rate of change is negative) on the interval (-0.74,0.54) and increasing everywhere else. So your answer is
(-∞,-0.74)U(0.54,∞)

If this is a calculus class, then just note that
f'(x) = 6(5x^2+x-2)
f(x) is increasing where f'(x) > 0 on the interval I noted above.