#### Question

Show that f(x) = x^{9} + 4x^{7} + 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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Solution for question: Show that F(X) = X9 + 4x7 + 11 is an Increasing Function for All X ∈ R ? concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)