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Question

Find the values of x, such that f(x)=2x315x2+36x+1 is an increasing function.

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Solution

f(x)=2x315x2+36x+1
f(x)=6x230x+36+0
f(x)=6(x25x+6)
=6(x22x3x+6)
=6[x(x2)3(x2)]
=6(x2)(x3)
f(x)=0
6(x2)(x3)=0
(x2)(x3)=0
x=2,3.

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