# What are the points of inflection, if any, of #f(x)=x^4-x^3+6 #?

##### 2 Answers

See explanation.

#### Explanation:

Point of inflection can be calculated as the zero(s) of the second derivative. Here we have:

If we look at the graph of

graph{12x^2-6x [-3.077, 3.08, -1.538, 1.54]}

The derrivative changes signs at both

Answer: **The function has 2 points of inflection:**

#### Explanation:

The points of inflection are when the graph of

The way to find whether

To take the second derivative of a function, just derive it twice.

By the way, power rule states that the derivative of a function such as

Now that we have the second derivative

Therefore, we know know that the points of inflection are at

This is the graph of

graph{x^4 - x^3 + 6 [-7.194, 8.616, -0.42, 7.48]}

This is the graph of

graph{4x^3 - 3x^2 [-9.29, 10.72, -4.11, 5.885]}

This is the graph of

graph{12x^2 - 6x [-9.29, 10.72, -4.11, 5.885]}