For what values of x is #f(x)=-x^3+x^2+2x+5# concave or convex?
To find where the equation is concave and convex we need to first find the first derivative using the power rule.
The first derivative is:
Now we find the second derivative:
We set it equal to zero and solve:
Now we create a test interval from
Then we pick a number from the left and right and plug it into our
Keep in mind that it can be any number I picked
Now if the number you get after plugging it in is positive then it means for that interval the graph is concave up. If the number is negative then the graph is concave down for that interval only.
So we can say that for