Answer to Question #258551 in Calculus for Olivia

Question

y'' of y = x^-2 at x=2

Answer 1

Let us find $y''$ of $y = x^{-2}$ at $x=2.$

It follows that $y'=-2x^{-3},\ y''=(-3)(-2)x^{-4}=6x^{-4}.$

Consequently, $y''(2)=6\cdot 2^{-4}=\frac{6}{2^4}=\frac{3}{2^3}=\frac{3}8.$