Playing with Graphs - 7
You are given the function :
f ( x ) = max ( e x , x 2 , x 4 )
The number of points where the function is non - differentiable is A
The number of points where the function is non - continuous is B
The number of zeroes of the function is C
Enter your answer as A + B + 2 C .
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1 solution
Hey i can only find 3 non differentiable pts..... pls help
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Agreed there are only 3 points where function is non differentiable
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Firstly there are 0 pts of discontinuity nd secondly , haven't u tried my 6th q
Tell me which all points u are getting. , not exactly points but give a clue
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@Aniket Sanghi – Firstly when − ∞ < x < − 1 then f ( x ) = x 4 after that f ( x ) becomes x 2 (1st point)
Then between 0 < x < 1 e x 'overtakes' x 2 (2nd point)
Finally later x 4 overtakes e x giving 3rd point.
I earlier meant non differentiable but wrote discontinuous by mistake :P
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@Neelesh Vij – Yup then afterwards e x will again overtake x 4 , you can check this by solving eq e x = x 4
@Neelesh Vij – Now after knowing the key feature abt this q , u must definetely like it :) Right!
@Neelesh Vij – But afterwards e x will overtake x^4
As for x>0 e x = x 4 has two solutions
At first intersection point x 4 overtakes e x
and at second intersection point of them e x overtakes x 4
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@Harsh Gupta – Are u really 15 yrs old
@Aniket Sanghi – Am I right or wrong please tell. The function max() is always continuous if we put continuous function in it.
Am I right or wrong please tell. The function max() is always continuous if we put continuous function in it.
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Yeah seems like that! But have to verify through examples.
Numerical solution: A=4 , B = 0 , C = 0
If you think that A=3, you are missing the point of the problem.
Hint: Exponential functions grow faster than polynomial functions.