A function assigns the values. The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
A function assigns the value of each element of one set to the other specific element of another set.
To find the point at which the function has the maximum value we need to differentiate the function. Therefore, the function can be written as,
[tex]f(x) = 2x^3 - 18x^2 + 48x - 1 \\\\\dfrac{d}{dx}f(x) = \dfrac{d}{dx}(2x^3 - 18x^2 + 48x - 1)\\\\f' = 6x^2-36x+48[/tex]
Equate the function with zero to know at what value of x the function returns a maximum value.
6x² - 36x + 48 = 0
x² - 6x + 8 = 0
x² -2x -4x +8 = 0
(x-2)(x-4)=0
Since we want to the value in the interval of 0 to 3, therefore, 2 is the value at which the function will have its maximum value.
f(2) = 2(2)³ - 18(2)² + 48(2) - 1
f(2) = 39
Hence, The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
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