If f(x) = kx3 – 69x2 + 9x + 3 is increasing on R, then – | MATH - INCREASING AND DECREASING FUNCTION | SolveeIt | Solveeit

Today, August 19

Question

If f(x) = kx³ – 69x² + 9x + 3 is increasing on R, then –

A

k < 3

B

k > 3

C

k £ 3

D

None

Answer

k > 3

Explanation

Solution

f(x) = 3kx² – 18x + 9 > 0

\begin{aligned} & 3k > 0 \\ & k > 0 \\ & \begin{matrix} k > 3 \end{matrix} \end{aligned} & \begin{aligned} & \because\mspace{6mu} D < 0 \\ & \Rightarrow 324–108k < 0 \\ & \Rightarrow \begin{matrix} k > 3 \end{matrix} \end{aligned} \end{matrix}$$