Question

If f(x)=13x3−4x2+12x−5 and the domain is the set of all x such that 0≤x≤9 , then the absolute maximum value of the function f occurs when x is

Answer 1

The correct format of the question is

If f(x)= $\frac{1}{3}x^3 -4x^2+12x -5$ and the domain is the set of all x such that 0≤x≤9 , then the absolute maximum value of the function f occurs when x is

Answer:

The absolute maximum value of the function F(x) occurs when x is 9

Step-by-step explanation:

F'(x) = $x^2 -8x +12= 0$

      = (x-6)(x-2) = 0

      x = 2,6

so we have boundary points 0 , 9 and 2,6

The value of function at these four points

  x =     0    2       6     9

F(x) =  -5    17/3   -5     22

So the absolute maximum value of the given function is x = 9 and F(x) is 22.