# How many stationary points can a cubic function have?

A cubic polynomial with real coefficients can have at most 2 real stationary points

We'll restrict our consideration to cubic polynomials with real coefficients in this case.

Examine the general cubic polynomial equation:

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

A cubic function can have at most two stationary points.

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

A cubic function can have a maximum of two stationary points. These stationary points occur where the derivative of the cubic function is equal to zero. Since a cubic function is a polynomial of degree three, its derivative is a quadratic function, which can have at most two real roots. Each real root corresponds to a stationary point on the cubic function's graph. Therefore, a cubic function can have up to two stationary points.

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

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.

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.

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.

- What is the derivative of a function equal to at a critical point?
- Is #f(x)=(x^3+3x^2-x-9)/(x+1)# increasing or decreasing at #x=-2#?
- What are the values and types of the critical points, if any, of #f(x)=xlnx#?
- How do you find all the critical points of the function #f(x) = x^3 − 12x + 7#?
- What are the critical points of #f(x) = x(x + 1)^3#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7