How do I find the local and extreme values of a function on a given interval.

Question

Find the local and absolute extreme values of the function on the given interval.  f(x)=3x/2x^2+5,  [0,3]

Answer 1

Given function f(x) = 3x/2x^2+5

Given interval a = 0, b = 3.

f(0) = 3(0)/2(0)^2+5 = 0

f(3) = 3(3)/(2(3)^2+5) = 9/21

f'(x) = f(b)-f(a)/b-a

= [(9/21)-0]/(3-0)

= 1/7.