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Question
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Solution
\[f\left( x \right) = x^9 + 4 x^7 + 11\]
\[f'\left( x \right) = 9 x^8 + 28 x^6 \geq 0, \forall x \in R \left[ \because x^8 {, x}^6 \geq0, \text { for } \forall x \in R \right]\]
\[\text {So, f(x) is increasing on R } .\]
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