For problems 3 and 4, you must use calculus techniques to analyze the following
ID: 2851723 • Letter: F
Question
For problems 3 and 4, you must use calculus techniques to analyze the following questions. You will not be awarded with any credit by simply plotting the graph of f(x) on a calculator and answer the following questions based on plotted graph However, you may use your calculator to sense. Consider the function: Find the critical point(s). Find the interval(s) of increase and/or decrease for the function f (x). Write your answer using interval notation(s). Find the local maximum and local minimum value(s). if exist(s). If not exist, explain why not.Explanation / Answer
for critical points , find f dash (x) =0
fdash(x) = 1 -cosx =0
=>cosx = 1
=> x = 0 -------this is the critical point
2) function is increasing is fdash(x) >0
so 1-cosx >0 => which is in interval [-pi /2 ,pi/2]
as it is increasing for total interval , there is no interval in which it decreases
3) f doubledash of x = sinx
put critical point x=0 , in f double dash x
sin(0) =0 ---------so no maximum / minimum exists
f has maxima or minima on if f double dash is not =0 at the critical points ------answer
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