Determine a differentiable function `y\ =\ f(x)` which satisfies `f\ (x)=[f(x)]^2\ a n d\ f\ (0)=\ -1/2dot` Find also the equation of the tangent at the point where the curve crosses the y-axis .

A differential function y=f(x) satisfies f(x)-(f(x))^(2)+5 and f(0)=1. Then the equation of tangent at the point where the curve crosses y-axis is

A differentiable function y=f(x) satisfies f'(x)=(f(x))^(2)+5 and f(0)=1. Then the equation of tangent at the point where the curve crosses y-axis,is

A function y=f(x) satisfying f'(x)=x^(-(3)/(2)),f'(4)=2 and f(0)=0 is

A polynomial function f(x) satisfies the condition f(x+1)=f(x)+2x+1. Find f(x) if f(0)=1 Findalso the equations of the pair of tangents from the origin on the curve y=f(x) and compute the areaenclosed by the curve and the pair of tangents.

Let f be a real valued differentiable function satisfying f(x+y)=f(x)+f(y)-xy-1,AA x,y in R and f(1)=1. Equation ofthe normal to the graph of f(x) at the point where y=f(x) cuts the y-axis,is

Let f(x) be a differentiable function which satisfies the equation f(xy)=f(x)+f(y) for all x>0,y>0 then f'(x) equals to

Let f be a real valued differentiable function satisfying f(x + y) =f(x) + f(y)-xy-1, AA x, y in R and f(1)=1. (i) Equation ofthe normal to the graph of f(x) at the point where y=f(x) cuts the y-axis, is (ii) area enclosed by the curve y=f(x) in the first quardrant:

Let f :[0,2p] to [-3, 3] be a given function defined at f (x) = cos ""(pi)/(2). The slope of the tangent to the curve y = f^(-1) (x) at the point where the curve crosses the y-axis is:

Let f :[0,2p] to [-3, 3] be a given function defined at f (x) = 3 cos ""(x)/(2). The slope of the tangent to the curve y = f^(-1) (x) at the point where the curve crosses the y-axis is: