Let f(x) be differentiable for real such that
`f'(x)gt0" on "(-oo,-4),`
`f'(x)lt0" on "(-4,6) and `
`f(x) gt 0" on "(6,oo).`
If `g(x)=f(10 - 2x)`, then the value of g'(2) is

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then

If f(x) is a differentiable real valued function satisfying f''(x)-3f'(x) gt 3 AA x ge 0 and f'(0)=-1, then f(x)+x AA x gt 0 is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :