Question

当 $x$ 取任意实数时， $8x-3x^2$ 的最大值为：

For any real value of $x$ the maximum value of $8x-3x^2$ is:

$0$

$\dfrac83$

$4$

$5$

$\dfrac{16}{3}$

对 $8x-3x^2$ 配方

Complete the square in $8x-3x^2$

负的平方项在等于 $0$ 时最大

A negative square is largest when it equals $0$

配方得 $8x-3x^2 =\frac{16}{3}-3\left(x-\frac43\right)^2\text{。}$ 平方项非负，所以最大值为 $\frac{16}{3}$ 。

所以正确答案是 E。

Completing the square, $8x-3x^2 =\frac{16}{3}-3\left(x-\frac43\right)^2.$ The square term is nonnegative, so the maximum is $\frac{16}{3}.$

Thus, the correct answer is E.