For what values of a, m and b, Lagrange's mean value theerorem is applicable to the fucntion f(x) for `x epsi[0,2],f(x)= {{:(3,,x=0),(-x^(2)+a,,altxlt1),(mx+b,,1lexle2):}`

Options

A. a=3, m=-2,b=0
B. a=3, m=-2,b=4
C. a=3, m=-2,b=4
D. No such a, m b exist

Answer

B

Explanation

`f(x)[{:(3,x=0),(a-x^(2),oltxlt1),(mx+b,1lexle2):}`
For Lagrange's mean value theorem f(x) must be continous in [0,2] and differentiable in (0,2)
Hence,a=3
m+b=2
`[{:(-2x,0ltxle1),(m,1ltxle2):}`
`rArrm=-2` and hence b=4