f(x)=1/2x^2-8x+1 find the value of x which satisfies the mean value theorem on the interval [2,8].

Question

I need to use my calculator on this part but i'm not sure how to. I used the formula to solve it but i'd like to know how to do it on the calculator also.

 

also, i'm not sure how to solve this.

f(x)=1/3x^3+5/2x^2+6x on [-5,2] find increasing/decreasing intervals, extrema (classify as max/min, absolute/local), pts of inflection, concave up/down intervals.