The value of x is 0.85. Then the value of f(x) is 12. Then the correct option is C.
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function f(x) is [tex]\dfrac{24}{1+3e^{-1.3x}}[/tex].
Differentiate the function with respect to x. we have
[tex]\dfrac{d}{dx} f(x) = \dfrac{468e^{\frac{13x}{10}}}{5(e^{\frac{13x}{10}}+3)^2}[/tex]
For the maximum value, the above equation equals zero.
[tex]\dfrac{d}{dx} f(x) = 0\\\\\\ \dfrac{468e^{\frac{13x}{10}}}{5(e^{\frac{13x}{10}}+3)^2}= 0\\\\\\ x = 8.5[/tex]
Then the value of f(x) is 12.
Thus, the correct option is C.
More about the differentiation link is given below.
https://brainly.com/question/24062595
