Find the critical points of $f(x)=-x^2$.

Primary tabs

Lesson Parent: 
Geometry of Functions VI: Critical Points
Problem: 

Find the critical points of $f(x)=-x^2$.

Answer: 

$x=0$ is the only critical point of $f(x)=-x^2$.

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

Critical points are where either <Sign in to see all the formulas> or <Sign in to see all the formulas> does not exist. We know that the derivative is <Sign in to see all the formulas> exists and is <Sign in to see all the formulas>. We now set <Sign in to see all the formulas>, divide both sides by $2$, and see that $x=0$ is the only critical point.