Find the absolute max/min values of : f(x)= (x-1)(x-7)^3+11 on the interval [1,4]. b.) interval [1,8] c.) [4,9]

Question

anonymous · Answer

Is this a calculus problem?

anonymous · Answer

Yes it is

anonymous · Answer

Take derivative and second derivative.  Where the derivative is zero will indicate a possible max or min.  If the second derivative is positive, that value of x is a minimum; if negative, a maximum.  Also, make sure to test the value of the function at the endpoints of the intervals, because the min or max might be there, even though the derivative isn't zero.

anonymous · Answer

Is that enough help?

anonymous · Answer

$$f(x)= (x-1)(x-7)^3+11$$$$f'(x)=(x-7)^3+3(x-1)(x-7)^2$$

anonymous · Answer

$$f"(x)=6(x-7)^2+6(x-1)(x-7)=12(x-7)(x-4)$$

anonymous · Answer

I see, I will try it from here. Thanks!

anonymous · Answer

My pleasure.