A line is tangent to the curve `f (x)=41/3 x^3` at the point `P `in the first quadrant, and has a slope `2009`. This line intersects the y-axis at `(0, b)`. Find the value of `b`

The slope of the tangent line to the curve x+y=xy at the point (2,2) is

Find the slope of the tangents to the curve y=x^2(x+3) at the points where it crosses the x-axis.

Find the slope of the tangent to the curve y=x^(3)-3x+2 at the point whose x-coordinate is 3 .

The slope of the tangent to the curve y=x^(2) -x at the point where the line y = 2 cuts the curve in the first quadrant, is

The slope of normal to the curve x^(3)=8a^(2)y, a gt 0 at a point in the first quadrant is -(2)/(3) , then point is

Equation of the tangent to the curve y=2x^(2)+5x , at the point where the line y=3 cuts the curve in the first quadrant , is

The tangents to the curve y=(x-2)^(2)-1 at its points of intersection with the line x-y=3, intersect at the point:

The area of the region bounded by the curve y ^(2) = x and the Y axis in the first quadrant and lines y= 3 and y = 9 " is "_________"

let T denote a curve y=f(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to T at a point P intersect the y-axis at Y_(P) and PY_P has length 1 for each poinit P on T. then which of the following option may be correct?