FOR EACH PROBLEM FIND THE FOLLOWING (SHOW ALL WORK & LABEL EACH PART AS STEP 1,

Question

FOR EACH PROBLEM FIND THE FOLLOWING (SHOW ALL WORK & LABEL EACH PART AS STEP 1, STEP 2, ETC.)

The book used for steps to be followed is:
TAN Applied Calculus For The Managerial, Life, & Social Sciences 9th Edition

Chapter 4 Problems

a) Find the intervals where the function f is increasing and where it is decreasing
b) Find the relative extrema of f
c) Find the intervals where the graph of f is concave upward and where it is concave downward
d) Find the inflection point, if any, of f


Problems:
1) f(x)= (x-2)^3
2) f(x)= x+(4/x)
3) f(x)= SQROOT x-1
4) f(x)= x SQROOT x-1
5) f(x)= (-1) / (1+x^2)

Explanation / Answer

i will show you work for any one question...rest you can do it yourself lets take 1st part f(x) = (x-2)^3 a) f'(x) = 3(x-2)^2 f'(x) is always positive hence f(x) is always increasing (b) put f'(x) = 0 to find critical point where extrema may exist 3(x-2)^2 = 0 x = 2 f''(x) = 6(x-2) since at x = 2, f''(x) = 0, hence we dont have extrema c) for concave up, f''(x) > 0 6(x-2) > 0 x>2.......for concave up x < 2.....for concave down d) inflection point exist at f''(x) = 0 hence x =2 is the inflection point

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