Consider the function f(x)=x2e4x. f(x) has two inflection points at x = C and x = D with C≤D where C is and D is Finally for each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD). (−[infinity],C]: [C, D]: [D,[infinity])

the inflection points are

So,

It is concave down at the intervals

And it would be concave up at

Step-by-step explanation:

Remember that to find inflection points you need to find where

Since

Then using the product and the chain rule you have that

And then, using again the chain rule and the product rule you have that

Therefore you have to solve the equation

Using the quadratic equation you get that there are two solutions, so the inflection points are

So,  

Now remember that a function is concave up if the derivative is greater than zero and concave down if the derivative is less than zero. Therefor you have to solve these inequalties

And you would get that is concave down at the intervals

And it would be concave up at

why can't you?

step-by-step explanation: