Let `y=f(x)` be a parabola, having its axis parallel to the y-axis, which is touched by the line `y=x` at `x=1.` Then, (a)`2f(0)=1-f^(prime)(0)` (b) `f(0)+f^(prime)(0)+f^(0)=1` (c)`f^(prime)(1)=1` (d) `f^(prime)(0)=f^(prime)(1)`

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0

If f(x)=|logx|,xgt0 ,find f^(prime)(1/e)a n df^(prime)(e)

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0, then (a) f(4)=f(-4) (b) f(2)+f(-2)=0 (c) f^(prime)(4)+f^(prime)(-4)=0 (d) f^(prime)(2)=f^(prime)(-2)

If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0, then (a)f(4)=f(-4) (b)f(2)+f(-2)=0 (c)f^(prime)(4)+f^(prime)(-4)=0 (d)f^(prime)(2)=f^(prime)(-2)

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,f(0)=3,f(pi/2)=5 . Find f(x).

If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=5 , find f(x) .

If f: RvecR is a twice differentiable function such that f"(x)>0fora l lxR ,a n d f(1/2)=1/2,f(1)=1 then: f^(prime)(1)>1 (b) f^(prime)(1)lt=0 (c)1/2 ltf^(prime)(1)lt1 (d)="" 0ltf^(prime)(1)lt="1/2

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is