If `f(x)=x^3+4x^2+lambdax+1` is a monotonically decreasing function of `x` in the largest possible interval `(-2,-2/3)dot` Then `lambda=4` (b) `lambda=2` `lambda=-1` (d) `lambda` has no real value

Options

A. `lambda=4`
B. `lambda=2`
C. `lambda=-1`
D. `lambda` has no real value

Answer

1

Explanation

Here f(x) `le` 0
or `3x^(2)+8x+lambda 0 forall x in (-2,(-2)/(3))`
Then situation for f(x) are as follows

Given that f(x) decreases in the largest possible interval
`(-2,(-2)/(3))` Then f(x) =0 must have roots -2 and `-2//3` Thus products of roots =`(2)(-2)/(3)=(lambda)/(3) or lambda=4`