P is a point on the curve `f(x)=x-x^(2)` such that abscissae of P lies in the interval `(0,1)` .The maximum area of the triangle POA,where and `A` are the points `(0,0)` and `(1,0)` is

A tangent is drawn to the parabola y^2=4a x at the point P whose abscissa lies in the interval (1, 4). The maximum possible area f the triangle formed by the tangent at P , the ordinates of the point P , and the x-axis is equal to 8 (b) 16 (c) 24 (d) 32

The points on the curve y=x^(2) which are closest to the point P(0, 1) are

The area bounded by the curve y= f(x) and the lines x=0, y=0 and x=t , lies in the interval

Find a point on the curve y=x^(2)+x, where the tangent is parallel to the chord joining (0,0) and (1,2).

The area of the triangle formed by normal at the point (1,0) on the curve x=e^( sin y with ) axes is

Find a point on the curve y=x^2+x , where the tangent is parallel to the chord joining (0, 0) and (1, 2).

If x_(1) and x_(2) are abscissae of two points on the curve f(x)=x-x^(2) in the interval (0,1). then maximum value of the expression (x_(1)+x_(2))-(x_(1)^(2)+x_(2)^(2)) is