Find the critical values f(x) on the given interval. f(x)= x/x^2-x+9, [0,9]

Question

Find the critical values f(x) on the given interval. f(x)= x/x^2-x+9, [0,9]

Answer 1

f(x) = x/(x² – x + 9)

Critical points occur where the first derivative of a function is equal to zero.

f'(x) = 0 when x = –3 or x = 3; only x = 3 is on the interval [0,9]

f(3) = 3/((3)² – 3 + 9) = 3/15 = 1/5

So the critical point on [0,9] is (3, f(3)) = (3, 1/5)