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

Concave (Convex) Up on the interval

Concave (Convex) Down on the interval

Find the First Derivative

Find the Second Derivative

Next, set

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

Refer to the Number Line as shown below:

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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.

- What are the points of inflection, if any, of #f(x)=2x^3+x^2+x+3 #?
- How do you find the inflection points of the graph of the function: #y=x^3-15x^2+33x+100#?
- Is #f(x)=sinx# concave or convex at #x=pi/5#?
- How do you use the first and second derivatives to sketch #y = x / (x^2 - 9)#?
- What is the second derivative of #f(x)= e^sqrt(3x-7)#?

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