# How do you determine whether the function #f(x)=x^8(ln(x))# is concave up or concave down and its intervals?

See the explanation.

The intervals of concavity are determined by 2nd derivative. If 2nd derivative changes sign in the points where it is equal to zero, those points are inflection points.

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

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.

- For what values of x is #f(x)=-x^2+e^x# concave or convex?
- How do you determine the intervals where #f(x)=x^(2/3)+3# is concave up or down?
- If #y = x^2 ln x#, what are the points of inflection, concavity and critical points?
- How do you find the first and second derivative of #(lnx)^2#?
- If #f '(x) = 8x^3 - 16x#, how do you use the second derivative test to find maximum and minimum?

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