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