Question

`2x^(3) - 6x + 5` is an increasing function, if
A. ` 0 lt x lt 1`
B. `-1 lt x lt 1`
C. ` x lt -1 or x gt 1`
D. `-1 lt x lt -(1)/(2)`

Answer 1

Correct Answer - C
`f(x)` is an increasing function , if `f(x) gt 0`
Let `f(x) = 2x^(3) - 6x + 5`
On differenting , w.r.t .x, we get
`f(x) = 6x^(2) - 6`
Since f(x) is increasing function.
`rArr " " 6x^(2) - 6 gt 0`
` rArr (x - 1) (x+1) gt 0`
` rArr " " x gt 1 or x lt -1 `