Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

How do you determine critical points for any polynomial?

Answer 1

by finding the first derivative of the polynomial and find the values of the variable at which the first derivative equals zero

for example: #y=x^2-2x# by finding the first derivative #y'=2x-2# so #y'=0# when #2x-2=0# and by solving it the #x# co_ordinate of the critical point of the function #=1# so the critical point will be #(1,-1)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emma Aldridge

To determine critical points for any polynomial, follow these steps:

Find the derivative of the polynomial using differentiation.
Set the derivative equal to zero and solve for the variable(s). These solutions are potential critical points.
Test each potential critical point by plugging it into the original polynomial. If the derivative changes sign at that point, it is a critical point. If not, it is not a critical point.
Repeat steps 2 and 3 for all potential critical points to find all critical points of the polynomial.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.