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The Function F (X) = X^3 – 3x^2 + 3x – 100, X∈ R is - Mathematics and Statistics

The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.

(A) increasing

(B) decreasing

(C) increasing and decreasing

(D) neither increasing nor decreasing

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Solution

(A) increasing

`f(x)=x^3-3x^2+3x-100, x in R`

`f'(x)=3x^2-6x+3`

`=3(x^2-2x+1)`

`=3(x-1)^2`

Since, (x – 1)2 is always positive x ≠ 1

f'(x) > 0 for all x ∈ R, x ≠ 1

Hence, f (x) is an increasing function, for all x ∈ R, x ≠ 1

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