If `x+ 7y =29` is an equation ofthe line normal to the graph of f at the point `(1,4)`, then `f'(1)` is equal 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. Equation ofthe normal to the graph of f(x) at the point where y=f(x) cuts the y-axis,is

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:

If m is the slop of the normal to the continous curve y=f(x) at the point (x_(1),y_(1)) , then m is equal to-

Suppose f(x) =(x+1)^(2) for x ge -1 . If g(x) is the function whose graph is the reflection of the graph of f(x) w.r.t the line y = x, then g(x) is equal to:

Equations of the tangent and normal to the curve x^(2)+y^(2)+4x-7y+5=0 at the point (1,2) are

Suppose f(x)=(x+1)^(2) for xge-1 . If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y=x , then g(x) equals :

If y=f(x) be the equation of a parabola which is touch by the line y=x at the point where x=1 then

If the normal to y=f(x) makes an angle of.(pi)/(4) in anticlockwise direction with positive y- axis at (1,1), then f'(1) is equal to

A curve y=f(x) passes through point P(1,1). The normal to the curve at P is a (y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point,then the equation of the curve is