Find the absolute maximum and minimum values of the function on the interval and their corresponding x-values.
f(x)=2x^3-3x^2-12x on [-2,3]

Question

Find the absolute maximum and minimum values of the function on the interval and their corresponding x-values. 
f(x)=2x^3-3x^2-12x on [-2,3]

anonymous · Answer

We can start by checking our endpoints and then take the derivative of f(x).

anonymous · Answer

f'(x)=6x^2-6x-12

anonymous · Answer

Yes; and, what are the function values for the end points of the interval we were given? We continue by finding the intervals where f(x) is increasing and decreasing. To do this, we set f'(x) equal to zero and observe the function values around the roots of f'(x).

anonymous · Answer

Look at the plot and try to prove what you can conclude from the graph http://www.wolframalpha.com/input/?i=Plot+2+x^3+-+3+x^2+-+12+x++from+x%3D-2+to+x%3D3++