PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for Prove that the Following Function is Increasing on R F ( X ) = 3 X 5 + 40 X 3 + 240 X ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

Prove that the following function is increasing on R f $(x) =$3 $x^5$ + 40 $x^3$ + 240$x$ ?

#### Solution

$f\left( x \right) = 3 x^5 + 40 x^3 + 240x$

$f'\left( x \right) = 15 x^4 + 120 x^2 + 240$

$= 15 \left( x^4 + 8 x^2 + 16 \right)$

$= 15 \left( x^2 + 4 \right)^2 > 0, \forall x \in R \left[ \because 15 > 0 \text { and } \left( x^2 + 4 \right)^2 > 0 \right]$

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Solution Prove that the Following Function is Increasing on R F ( X ) = 3 X 5 + 40 X 3 + 240 X ? Concept: Increasing and Decreasing Functions.
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