Find the relative extreme points of the tunction, it they exist Then skelch a gr

Question

Find the relative extreme points of the tunction, it they exist Then skelch a graph of the functon Idontily al the relative maximurn points Select the correct choice below and, if necossary, fil in le answer boxtes) lo complel your choce. OA. The relative mamumponis) isee Simplity your answer. Use inlegers or fractions for any numbers in the expression. Type an ordered par Use a comma to separale answers as needed) B. There are no relative maumum ports Identify all the relalive minimum points Select te corect choice below and, id necessary, fit in the answer bones) lo compele your choice O A. The relative minimum point(s) isare B. There are no relative mnnum points Choose the correct graph below O A (Simplity your answer Use integevs or tractions for any numbers in the expression. T ype an ordered pair Use a comma to sepatale answers as needecd D. C. Click to select your answer Save for Later /30/2017 e here to search

Explanation / Answer

Q.1 F(x) = (x-3)1/3

f'(X) = 1/3 (x-3)-2/3

f'(X) = 0 for relative minimum points

= > 1/3(x-3)-2/3 =0

so for no value of x the f'(X) where f'(x) is zero here so there are no mimum relative points.

Graph B is correct here out of 4 option.

Question 2.

f(x) = 4x + 2 ; x E [-4.5]

Here the abolute minimum value is (-4 * 4 +2 = -14) and absolute maximum value is (4 * 5 + 2 = 22)

so option A is correct.

Question 3 .

G(X) = -x3 + 2x2 + 15x + 3

G'(x) = -3x2 + 4x + 15

so G'(x) = 0

-3x2 + 4x + 15 = 0

x = -5/3, 3

f''(X) = -6x + 4 so

f''(-5/3) = 14; f'(3) = -14

so one relative minimum point that is x = -5/3 and the f(X)minimum = -11.8148

One relative mimimum point that is x = 3 and f(x)maximum = 39

Graph C is correct.

Question 4

C(X) = 4800 + 200X

R(X) = -x2 /2 + 400x

P(X) = R(X) - C(X) = -x2 /2 + 200x - 4800

Profit will be maximum when P'(x) = 0 and P''(x) =-ve

soP'(x) = -x + 200 and P''(X) = -1 (-ve)

so at x = 200 it will be maximum

P(200) = -(200)2 /2 + 200 * 200 - 4800 = $ 15200 (answer of part C)

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