# For what values of x is #f(x)= xe^-x # concave or convex?

We need to solve the inequality:

so we start by calculating the second derivative of the function:

using the product rule:

and again:

Now to solve the inequality we need to consider that:

graph{xe^(-x) [-10, 10, -5, 5]}

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.

- Consider the curve #y = (x^2- 2x+k)(x-6)^2 #, where #k# is a real constant. The curve has a maximum point at # x =3#. What is the value of #k#?
- What are the points of inflection, if any, of #f(x)= x^5 -2 x^3 - x^2-2 #?
- If #y = 3x^5 - 5x^3#, what are the points of inflection of the graph f (x)?
- What are the points of inflection of #f(x)=x^7/(4x-2) #?
- For what values of x is #f(x)=3x^3+2x^2-x+9# concave or convex?

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