Question 127

The maximum value of the expression $$2 + 8x - x^2$$ is

Solution

After differentiating and equating to 0,

8 - 2x = 0

$$\Rightarrow$$ 2x = 8

$$\Rightarrow$$ x = 4

$$\therefore\ $$The maximum value of expression occurs at x = 4.

When x = 4,

$$2+8x-x^2=2+8\left(4\right)-4^2=2+32-16=18$$

Hence, the correct answer is Option C

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