find all critical points of the function

Question

Find all critical points of the function f(x)=x^3+7x^2−7x−3. If there is more than one critical point, list them in descending order and separate them by commas.

 

Critical points=________

Answer 1

Set f'(x) = 0

 

3x² + 14x - 7 = 0

 

 

Use the quadratic formula:

 

x₁ = (-b - √(b² - 4ac)) / 2a            and             x₂ = (-b + √(b² - 4ac)) / 2a

 

where:

a = 3

b = 14

c = -7

 

Your critical points are then  (x₂ , f(x₂))  and   (x₁ , f(x₁))