Find the maximum value of $11 + 9 x - 7 x ^ { 2 }$ Restrict your attention to the horizontal span of 0 to 9.
A) 0.64
B) 13.89
C) 2.07
D) 17.5

Question

Quizplus · Accepted Answer

We are given an equation in terms of x and asked to find the maximum value of the equation on the interval from 0 to 9. To do this, we will take the derivative of the equation and set it equal to 0 to find the critical point(s) where the maximum or minimum occurs.

$$f(x) = 11 + 9x - 7x^2$$

Taking the derivative:

$$f'(x) = 9 - 14x$$

Setting equal to 0:

$$9 - 14x = 0$$
$$x = \frac{9}{14}$$

This critical point occurs within the given interval, so we will check the value of the function at that point and at the endpoints of the interval (0 and 9).

$$f(0) = 11 + 0 - 7(0)^2 = 11$$
$$f(9) = 11 + 9(9) - 7(9)^2 = -352$$
$$f(9/14) = 11 + 9\left(\frac{9}{14}\right) - 7\left(\frac{9}{14}\right)^2 \approx 13.89$$

Therefore, the maximum value of the function on the interval from 0 to 9 occurs at x = 9/14, and is approximately 13.89. The correct answer is B.

Find the Maximum Value Of 11+9x−7x211 + 9 x - 7 x ^ { 2 }11+9x−7x2

Find the Maximum Value Of $11 + 9 x - 7 x ^ { 2 }$