How can I calculate the extrema of a function (Minima and Maxima)?

Question

I am studying Calculus and I need help doing this. Any advice that is detailed and explanatory?

Answer 1

1. Differentiate the function. -- this gives the rate of change.
2. Set the derivative equal to 0. -- you want this because the rate of change = 0 at local extemes.
3. Solve for x. -- this is your answer, BUT --
4. Also check the endpoints. -- Sometimes the endpoints are the extreme values, but the derivative is not zero.\

Answer 2

Take the derivative and find its zeros.
Study the sign of the derivative at both sides of the zeros.
if the sign changes from - to + you have a local minimum
If the sign changes from+to- you have a local maximum
If the sign does not change there is NO extrema.
Instead of this you can take the value of the second derivative at
each zero of the first derivative
If the value is positive you have a minimum and if it is negative you have a maximum(local)