1.

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

Answer»

`(B-c)/(c-a)`
`(c-a)/(b-c)`
`(b-c)(c-a)`
`(1)/((b-c)(c-a))`

Solution :Let `u in (a,c), v in (c,b)`
Then by LMCT on (a, c), (c, b), we have
`f'(u)=(f(c)-f(a))/(c-a),f'(v)=(f(b)-f(c))/(b-c)`
But `u LT v and f''(x)lt 0, AA x in (a,b)`
`"i.e."f'(u)GTF'(v)`
`rArr""(f(c)-(a))/(f(b)-f(c))gt(c-a)/(b-c)`


Discussion

No Comment Found

Related InterviewSolutions