Question

1. if ( f(x)=(x^{2}-1)(x^{2}+1) ), then ( f^{prime}(-1)= ) (a) -4 (b) -2 (c) 2 (d) 4

Explanation:

Step1: Expand the function

$$\begin{align*} f(x)&=(x^{2}-1)(x^{2}+1)\\ &=x^{4}-1 \end{align*}$$

Step2: Differentiate the function

Using the power rule \((x^n)^\prime = nx^{n - 1}\), for \(y = x^{4}-1\), we have \(f^\prime(x)=4x^{3}\)

Step3: Substitute \(x=-1\)

Substitute \(x = - 1\) into \(f^\prime(x)\), \(f^\prime(-1)=4\times(-1)^{3}=-4\)

Answer:

A. \(-4\)