Consider the following function: f(x) = x^4 +6x^2
a. Determine the intervals of increasing and decreasing
b. Determine the local maximum and minimum
c. Determine the intervals of concave up and concave down
d. Determine the point of inflection

What do YOU think ?

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first and second derivatives.

This problem is very straight forward. The graph is easy to deal with. It is easy to see where it increases and decreases.

You can tell a lot from the graph.

Is it concave down anywhere?

The point of inflection is where it changes concavity. Does it change concavity? If not, then no inflection point(s).

But you can also check that by finding the second derivative, set it to 0 and solve for x.

f'(x)=4x^{3}+12x

f''(x)=12x^{2}+12

Now, there is more than enough info to finish up.