finding critical points and abs max min for function over given interval. urgent.

[bradcatjones]

Please help me with this question, I have a quiz tomorrow. Find critical points and absolute maximum and minimum for each function over the give interval. y=2x^3-6x, [0,3] also y= cubedroot of 1-x, [0,9]

 

[MarkFL]

What would you do to attempt these problems?

 

[Jason76]

In order to find critical points, the first derivative of the function is set to 0. Next, we solve for the x values (critical points).

Later, we can decide whether or not each point is a maximum or minimum with the 2nd derivative test. We plug each x value point into the 2nd derivative. If the answer (solving for f(x) is negative, then it's a maximum and that portion of the function is concave down. On the other hand, if the answer (solving or f(x)) is positive, then it's a minimum, and that portion of the curve is concave up.