Please follow the instructions below for these four functions! For the four funt

Question

Please follow the instructions below for these four functions!

For the four funtions:

Do the following:

(1) Find the intervals of increase and decrease

(2) Find the local maxima and minima

(3) Find the intervals on which the function is concaveup and concave down

(4) Find any inflection points

(5) Sketch the graph

Please follow the instructions below for these four functions! For the four funtions: a) f(x)=x^3-12x^2-36x b)f(x)=5x^(2/3)-2x^(5/3) c) f(x)=x+2sin(x)[0,2Pi] d) f(x)=x/x-1 Do the following: (1) Find the intervals of increase and decrease (2) Find the local maxima and minima (3) Find the intervals on which the function is concaveup and concave down (4) Find any inflection points (5) Sketch the graph

Explanation / Answer

a)

1. Increasing at x (-infinity , -1.3) U (9.3 , infinity)

decreasing for x (-1.3 , 9.3)

2. local maxima at x= -1.3

local minima at x= 9.3

3. convave up at x (9.3 , infinity)

concave down at x (- infinity , 9.3)

4. inflection point at x= 9.3

b.

1. its decreasing for all x E R real numbers

2. no maxima or minima (local)

3. concave up x (- infinity , 0)

concave down x (0 , infinity)

4. inflection point x=0

c.

1. increasing at x (0 , 2pi/3) U (4pi/3 , 2pi)

decreasing at x (2pi/3 , 4pi/3)

2. local maxima at x= 2pi/3 and at x=2pi

local minima at x=0 and x= 4pi/3

3.

concave up at x (4pi/3 , 2pi

concave down at x (0 , 4pi/3)

4. inflection point at x = 4pi/3

d.

1. its decreasing for all x values except x=1 as it not defined at x=1

2. no maxima or minima

3.

concave up for x (1 , infinity)

concave down for x (-infinity , 1)

4. inflection point at x=1

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