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Question

The maximum value of f(x)=100|45x| for any value of x is kx then k is ____.

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Solution

Given f(x)=100|45x|

Case 1- 45x>0
|45x|=45x

f(x)=100(45x)
f(x)=10045+x

y=f(x)=55+x (1)

Case 2- 45x<0
|45x|=(45x)
|45x|=x45

f(x)=100(x45)
f(x)=100x+45
y=f(x)=145x (2)

Equate equations (1) and (2),

55+x=145x
2x=14555
2x=90
x=45

Thus, maximum function is given by,

f(x)=55+x for x>45
f(x)=145x for x<45

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