Question

Show that f(x) = x⁹ + 4x⁷ + 11 is an increasing function for all x ∈ R.

Answer 1

$$\begin{gathered} f\left(x\right)=x^9+4x^7+11 \\ f\text{'}\left(x\right)=9x^8+28x^6\ge 0,\forall x\in R\left[\text{∵}{\mathit{\text{x}}}^8{\mathit{\text{, x}}}^6\text{≥0, for ∀}x\in R\right] \\ \text{So,}\mathit{\text{f}}\text{(}\mathit{\text{x}})\text{is increasing on}R. \end{gathered}$$