Thread: The mean value theorem

Hello there, could you help me:

Problem 27, Apostol, Calculus

For real t , f(x)=-(1/3)x^3+ t^2(x), where m(t) is the minimum of f(x), in 0<=x<=1, what is m(t) in -1<=t<=1

It's just like the other problems you've been doing, but your calculations have "t" in them. So find the critical points (x=0, x=1, and wherever f'(x) is zero) and see which of them gives the minimum. Your answer might be different for different ranges of t.

- Hollywood

thanks, i have to check. . .