If the average rate of change is 18, then the value of the x is √(13/5). Then the correct option is B.
It's an average of how far the functions changed per unit throughout that time period.
Let f be the function given by f(x) = x³ + 5x.
Then the value in the closed interval [1,3] will be
The instantaneous rate of change will be
[tex]f'(x) = 3x ^2 + 5[/tex]
Then the average rate of change will be
[tex]= \dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{(3^3 + 5\times 3) - (1^3 + 5 \times 1)}{3-1}\\\\= 18[/tex]
Then we have
3x² + 5 = 18
Then the value of x will be
[tex]\begin{aligned} \rm 3x^2 + 5 &= 18\\\\\rm x &= \sqrt{\dfrac{13}{3}} \end{aligned}[/tex]
More about the average rate of change link is given below.
https://brainly.com/question/24062595
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