Application of Derivative Questions

Let f(x) = x sin π x, x > 0. Then for all natural numbers n, f′(x) vanishes at -

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio of 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four co...

Angle between the tangents to the curve y = x2 - 5x + 6 at the points (2, 0) and (3, 0) is

The d.r. of normal to the plane through (1, 0, 0) , (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are

The length of the subtangent at any point of the curve xmyn = am+n is proportional to-

If f(x) = , then-

If f′(x) = |x| - {x}, where {x} denotes the fractional part of x, then f(x) is decreasing in :-

If tangent to the curve y = f (x) at any point is parallel to y - axis , then at that point dy/dx equals-

If normal to the curve y = f (x) at a point makes 135o angle with x-axis, then at that point dy/dx equals-

The slope of the tangent to the curve x2 + 2y = 8x − 7 at the point x = 5 is -

The equation of the tangent to the curve y = cos x at x = π/3 is-

The equation of the tangent to the curve 6y = 7 − x3 at point (1, 1) is-

The equation of the tangent to the curve 1/√x + 1/√y = 2/√a at point (a, a) is-

If tangent at a point of the curve y = f (x) is perpendicular to 2x − 3y = 5 , then at that point dy/dx equals-

At what point the tangent to the curve √x + √y = √a is perpendicular to the x- axis-

At what point of the curve y = 2x2 − x + 1 tangent is parallel to y = 3x + 4 -

If tangent of the curve x = t2 − 1, y = t2 − t is perpendicular to x- axis, then-

The equation of tangent to the curve y = 1 − ex/2 at the point where it meets y- axis is-

The point where the tangent line to the curve y = e2x at (0,1) meets x- axis is-

At what point the slope of the tangent to the curve x2 + y2 − 2x − 3 = 0 is zero-