Question

The function f(x) = x⁹ + 3x⁷ + 64 is increasing on
(a) R
(b) (−∞, 0)
(c) (0, ∞)
(d) R₀

Answer 1

(a) R

$$\begin{gathered} f\left(x\right)=x^9+3x^7+64 \\ f\text{'}\left(x\right)=9x^8+21x^6>0,\forall x\in R \\ \text{So,}\mathit{\text{f}}\text{(}\mathit{\text{x}})\text{is increasing on}R. \end{gathered}$$