Application of Derivatives 4 Question 66

69. The maximum value of the function f(x)=2x315x2+36x48 on the set A=xx2+209x is

(2009)

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Solution:

  1. Given, A=xx2+209x=xx[4,5]

Now, f(x)=6(x25x+6)

Put f(x)=0x=2,3

f(2)=20,f(3)=21,f(4)=16,f(5)=7

From graph, maximum value of f(x) on set A is f(5)=7.

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