# For what values of x is #f(x)= -x^3+3x^2-2x+2 # concave or convex?

##### 1 Answer

Concave (Convex) Up on the interval

Concave (Convex) Down on the interval

#### Explanation:

We are given the function

Find the First Derivative

Find the Second Derivative

Next, set

Simplifying, we get

Then, we consider a number larger than 1 and a number smaller than 1 and substitute the values in our Second Derivative.

If the number is Greater than 1, our

If the number is Less than than 1, our

Hence, we observe that

Refer to the Number Line as shown below:

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1
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Positive Negative
```