PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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Solution for Prove that the Function F(X) = X3 − 6x2 + 12x − 18 is Increasing on R ? - PUC Karnataka Science Class 12 - Mathematics

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Question

Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?

Solution

\[f\left( x \right) = x^3 - 6 x^2 + 12x - 18\]

\[f'\left( x \right) = 3 x^2 - 12x + 12\]

\[ = 3\left( x^2 - 4x + 4 \right)\]

\[ = 3 \left( x - 2 \right)^2 \geq 0, \forall x \text { in R } \left[ \because 3 > 0 \text { &} \left( x - 2 \right)^2 \geq 0 \right]\]

\[\text { So,f(x)is increasing on R } .\]

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Solution Prove that the Function F(X) = X3 − 6x2 + 12x − 18 is Increasing on R ? Concept: Increasing and Decreasing Functions.
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