Respuesta :
The correct format of the question is
If f(x)= [tex]\frac{1}{3}x^3 -4x^2+12x -5[/tex] 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) = [tex]x^2 -8x +12= 0[/tex]
= (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.
The absolute maximum value of the function f occurs when x is 9 and this can be determined by differentiating f(x) and then equating it to zero.
Given :
- [tex]\rm f(x)=\dfrac{1}{3}x^3-4x^2+12x-5[/tex]
- The domain is the set of all x such that 0≤x≤9
In order to determine the absolute maximum value of function f(x), differentiate f(x) and then equate it to zero.
[tex]\rm f'(x)=\dfrac{1}{3}\times(3x^2)-8x+12[/tex]
Now, equate the above equation to zero.
[tex]x^2-8x+12 = 0[/tex]
Factorize the above quadratic equation.
[tex]x^2-6x-2x+12=0[/tex]
x(x - 6) - 2(x - 6) = 0
(x - 6)(x - 2) = 0
Now, determine the value of f(x) at x = 0, 2, 6, 9
f(0) = -5
f(2) = 1/3.(8) - 4(4) + 12(2) - 5
f(2) = 17/3
f(6) = 72 - 144 + 72 - 5
f(6) = -5
f(9) = 243 - 324 + 108 - 5
f(9) = 22
So, the absolute maximum value of the function f occurs when x is 9.
For more information, refer to the link given below:
https://brainly.com/question/24898810
