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Prove that the Following Function is Increasing on R F ( X ) = 3 X 5 + 40 X 3 + 240 X ?

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प्रश्न

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

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उत्तर

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

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

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

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

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अध्याय 16: Increasing and Decreasing Functions - Exercise 17.2 [पृष्ठ ३५]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 16 Increasing and Decreasing Functions
Exercise 17.2 | Q 30.1 | पृष्ठ ३५

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