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The graph of a function y=g(x) is shown ...

The graph of a function `y=g(x)` is shown in the following figure. If `f(x)=-3x^2-k x-12 ,k in Ra n df(g(x))>0AAx in R` then lest integral value of `k` is equal to a. b. c. d.

A

13

B

14

C

15

D

16

Text Solution

Verified by Experts

The correct Answer is:
C
`g(x) in [-2,-1] AA x in R`
`f(x)=-3x^(2)-kx-12`
`rArr" "f(0)=-12`
`because" "f(g(x)) gt 0 AA x in R`
`therefore" "f(-2) gt 0 and f(-1) ge0`
`{:(f(-2)gt0rArr-12+2k-12gt0rArrkgt12),(f(-1)ge0rArr-3+k-12ge0rArrk ge15):}}rArrkge15`
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