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Question

f(x)=x36x2+12x16 is strictly decreasing for

A
xR
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B
xR{1}
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C
xR+
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D
xϕ
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Solution

The correct option is D xϕ
A function is strictly decreasing in the range when d(f(x))dx<0
d(f(x))dx=3x212x+12=3(x24x+4)=3(x2)2
Since the square of any number is non negative, we don't find any value of x for which the function would be strictly decreasing.

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