### Home > CALC > Chapter 5 > Lesson 5.1.2 > Problem5-15

5-15.

Find the second derivative with respect to $x$ for each function.

1. $y = (x − 10)^2$

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

1. $g(x) =-5x + 10$

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

1. $y = 5x^8-3x^{-8}$

Use the Power Rule.