calc- work please help

Question

Consider the function 

The absolute maximum of  (on the given interval) is at  =   

and the absolute minimum of  (on the given interval) is at  =   

Answer 1

By taking the derivative of f we find that at x=5/3 the derivative is zero. Also for x<5/3 f'(x)<0 and for x>5/3 f'(x)>0. Hence, we have a local minimum at 5/3 which gives the value of f(5/3)=8-25/3. Evaluating f(x) at the end points of the interval [0,10] we obtain that f(0)=8 and f(10)=208. So we have a global maximum at x=10 and a global minimum at x=5/3.