Application of Derivatives questions
910 published questions with worked solutions.
- A tank with a rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 4 meter and...
- The angle between the tangents to the curves y=2x^2 and x=2y^2 at (1, 1) is
- If x = -1 and x = 2 are extreme points of f(x)= x+ x^2+x, and are constants, then the value of ^2+2 is
- The function f(x)= ^4x+ ^4x is increasing in
- A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of 10 cm/s, then the angle between...
- Let f(x) be the differentiable function for all x such that f'(x) 5 and f(1)=4. The maximum value of f(5) is …
- If the tangent to the curve 2y^3=x^3+ax^2 at the point (a,a) cuts off intercepts and on the coordinate axes such that ^2+ ^2=61,...
- If Rolle's theorem is applicable for the function f(x)= ( x^2+a x ) on [3, 4] with c [3,4] such that f'(c)=0, then the value of...
- If x+1 x^2+1 dx= ^ -1 x+g(x)+c, where c is constant of integration, then the function g(x) is monotonically increasing in the...
- If a spherical balloon has a variable diameter 3x+ 92 units, then the rate of change of its volume with respect to x is
- A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The...
- The equation of the normal to the curve xy+7=0 is Ax+By+C=0, then
- Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water...
- A(1, -3), B(4, 3) are two points on the curve y=x- 4 x . The points on the curve, the tangents at which are parallel to the chord...
- Slope of the tangent to the curve y=2e^x ( 4 - x 2 ) ( 4 - x 2 ) where 0 x 2 is minimum at x =
- If slope of the tangent to the curve xy + ax + by = 0 at the point (1, 1) on it is 2, then the value of 3a + b is
- The slope of the normal to the curve x= t and y=t- 1 t at t = 4 is
- Values of c as per Rolle's theorem for f(x)= x+ x+6 on [0,2 ] are
- A right circular cone has height 9cm and radius of base 5cm. It is inverted and water is poured into it. If at any instant, the...
- The function f(x) = x^3 - 6x^2 + 9x + 2 has maximum value when x is
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