PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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Solution for Prove that the Function F Given by F(X) = X3 − 3x2 + 4x is Strictly Increasing on R ? - PUC Karnataka Science Class 12 - Mathematics

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Question

Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?

Solution

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

\[f'\left( x \right) = 3 x^2 - 6x + 4\]

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

\[ = 3\left( x^2 - 2x + 1 \right) - 3 + 4\]

\[ = 3 \left( x - 1 \right)^2 + 1 > 0, \forall x \in R\]

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

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Solution Prove that the Function F Given by F(X) = X3 − 3x2 + 4x is Strictly Increasing on R ? Concept: Increasing and Decreasing Functions.
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