### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.2 > Problem5-15

5-15.

Write the second derivative with respect to $x$ for each function. Homework Help ✎

1. $y = \left(x – 10\right)^{2}$

This is the equation of a parabola. The $2$nd derivative represents the concavity of the original equation.
Is $y=\left(x−10\right)^2$ concave up, concave down or neither?

2. $g\left(x\right) = –5x + 10$

$g\left(x\right)$ is a linear equation.
$g ^{\prime \prime}\left(x\right)$ represents its concavity.
Is a straight line concave up, concave down or neither?

3. $y = 5x^{8} – 3x^{–8}$

Use the Power Rule.