we are given
(a)
Firstly, we will find critical numbers
so, we will find derivative
now, we can set it to 0
and then we can solve for x
we get
now, we can draw a number line and then locate these values
and then we can find sign of derivative on each intervals
increasing intervals:
Decreasing interval:
(b)
Local maxima:
It is the value of x where function changes from increasing to decreasing
so, local maxima is at
Local minima:
It is the value of x where function changes from decreasing to increasing
so, local minima is at
now, we will plug critical numbers and end values into original function
and we get
At x=0:
At :
At :
At :
Global maxima:
It is the largest value among them
so, we get
Global minima:
It is the largest value among them
so, we get
(c)
now, we can find second derivative
now, we can set it to 0
and then we can solve for x
so, we get
now, we can draw number line and locate these values
and then we can find sign of second derivative on each intervals
concave up intervals:
Concave down intervals:
Turning points:
All values of x for which concavity changes
so, we get turning points at