Question

1. calculator active. estimate the rate of change of f(x)=x^2 - x at x = - 1

Explanation:

Step1: Find the derivative of f(x)

The derivative of \(y = f(x)=x^{2}-x\) using the power - rule \((x^n)^\prime=nx^{n - 1}\). The derivative \(f^\prime(x)=(x^{2}-x)^\prime=(x^{2})^\prime-(x)^\prime\). So \(f^\prime(x)=2x - 1\).

Step2: Evaluate the derivative at x = - 1

Substitute \(x=-1\) into \(f^\prime(x)\). We get \(f^\prime(-1)=2\times(-1)-1=-2 - 1=-3\).

Answer:

-3