Playing with Graph --- 1

Calculus Level 5

f ( x ) = ( x 2 2 x ) ( 2 x 2 5 x 3 ) ( 2 x 2 + 3 x 2 ) ( 14 x 45 x 2 ) \large{f (x) = \dfrac{(x^2 - 2x )( 2x^2 -5x -3)}{( 2x^2 + 3x -2)( 14x - 45 - x^2)}}

If the number of points where the above function is not continuous is A A (also count the real numbers where the function is undefined), the number of local maxima is B B , the number of local minima is C C and number of integers not included in range is D D . All A A , B B , C C and D D are whole numbers.

Enter your answer as A + B 2 + C 3 + D 4 A + B^2 + C^3 + D^4 .


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The answer is 16.

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1 solution

Aniket Sanghi
Apr 28, 2016

A = 4 , B = 2 , C = 2 , D = 0

How D=0 D=4

Sahil Silare - 4 years, 4 months ago

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Graph added..

Aniket Sanghi - 4 years, 3 months ago

B must be 1 not 2 as by drawing graph there are only three points where dy/dx=0 and only one of them is local maximum .Points where dy/dx=0 are between (-1/2,0);(2,3);(5,9). Please check and tell me if I am getting wrong.

puneet mangla - 4 years, 4 months ago

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This was an argument in report by some senior , he made me realise that there is one more point in graph where the graph is taking a turn . I don recall it now but if you check the function values at some points you will get that exceptional point. (There is no way other than Checking! )

Aniket Sanghi - 4 years, 4 months ago

Graph added...

Aniket Sanghi - 4 years, 3 months ago

Can you add a more comprehensive solution, so that those who were unable to solve this problem can learn how to do so?

Calvin Lin Staff - 4 years, 3 months ago

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Sure , i can add a pic of the graph! :)

Aniket Sanghi - 4 years, 3 months ago

D =0 is not understood!!! What do you mean by points not included in rnge? and what is the range it is (- inf,+inf)

Arijit Dey - 3 years, 4 months ago

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Yeah! That means it's Range is R , means every point on Real axis is in its Range

Aniket Sanghi - 3 years, 3 months ago

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oh I got confused//\//\

Arijit Dey - 3 years, 3 months ago

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