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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 ? - CBSE (Commerce) Class 12 - Mathematics

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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 for question: Prove that the Following Function is Increasing on R F ( X ) = 3 X 5 + 40 X 3 + 240 X ? concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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