# How do you find the range of y=4x²-5x+2?

Jun 10, 2018

$y \ge \frac{7}{16}$

#### Explanation:

We get

$y ' \left(x\right) = 8 x - 5$
$y ' ' \left(x\right) = 8$
So we get

$y \left(\frac{5}{8}\right) = 4 \cdot \frac{25}{64} - \frac{25}{8} + 2 = \frac{7}{16}$

Since we have for $x = \frac{5}{8}$ a minimum, so we get

$y \ge \frac{7}{16}$