What are the local extrema of #f(x)= -x^3 + 3x^2 + 10x + 13#?
Local maximum is
Local minimum is
To find local extrema, we can use the first derivative test. We know that at a local extrema, at the very least the function's first derivative will equal zero. So, let's take the first derivative and set it equal to 0 and solve for x.
This equality can be solved easily with the quadratic formula. In our case,
Quadratic formula states:
If we plug back our values into the quadratic formula, we get
Now that we have the x values of where the local extrema are, let's plug them back into our original equation to get: