`f: [0, 2] rarr R` दो बार अवकलनीय फलन इस प्रकार है कि सभी `x in (0,2)` के लिए `f'' (x) gt 0` है। यदि `phi (x) = f(x) + f(2-x)` है, तो `phi`

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

If f(0)=2, f'(x) =f(x), phi (x) = x+f(x) then int_(0)^(1) f(x) phi (x) dx is

यदि f' (a) विधमान है तब lim_(x to a) (x f(a)-a f(x))/(x-a)=

Let f(x) = 2^(2x - 1) and phi(x) = -2^(x) + 2x "log" 2. If f'(x) gt phi'(x) , then

Let f(x)=2^(2x-1) and phi(x)=-2^(x)+2x log2 If f'(x)>phi(x), then

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 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

If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int_(0)^(1)f(x)phi(x)dx is