Application of Derivatives questions
910 published questions with worked solutions.
- An open metallic tank is to be constructed, with a square base and vertical sides, having volume 500 cubic meter. Then the...
- A square plate is contracting at the uniform rate 4 cm^2/ sec, then the rate at which the perimeter is decreasing, when side of...
- A ladder of length 17m rests with one and against a vertical wall and the other on the level ground. If the lower end slips away...
- If the line ax + by + c =0 is a normal to the curve xy = 1 then
- A kite is 120m high and 130m of string is out. If the kite is moving away horizontally at the rate of 39m/sec, then the rate at...
- The Number of values of C that satisfy the conclusion of Rolle's theorem in case of following function f(x)= 2 x, x [-1,1] is
- An open tank with a square bottom, to contain 4000 cubic cm. of liquid, is to be constructed. The dimensions of the tank, so that...
- The function f(x)=2x^3-9x^2+12x+2 is decreasing in
- The curve x^4-2xy^2+y^2+3x-3y=0 cuts the X-axis at (0, 0) at an angle of
- A point moves along the arc of parabola y = 2x^2. Its abscissae increases uniformly at the rate of 2 units/sec. At the instant,...
- The equation of the normal to the curve y = xlogx, which is parallel to the line 2x - 2y + 3 = 0, is
- The approximate value of x^3-2x^2+3x+2 at x = 2.01 is
- Local maximum and local minimum values respectively of the function f(x)=(x-1)(x+2)^2 are
- For every value of x [1, 3] the function f(x) = 1 8^x is
- The curve ( x a )^n + ( y b )^n = 2, n N touches the line at the point (a, b) then the equation of the line is
- The radius of a cylinder is increasing at that rate 2 cm/sec and its height is decreasing at the rate of 3 cm/sec, then the rate...
- Let x_0 be the point of local maxima of f(x)= a ( b c ) where a =x i -2 j +3 k , b =-2 i +x j - k and c =7 i -2 j +x k then the...
- The value of k such that the function f(x)= x- x-kx+b is strictly decreasing for all real x is
- The tangent to the curve y^2-xy+9=0 is vertical when
- If the function f(x)=ax^3+bx^2+11x-6, defined on [1, 3], satisfies all the conditions of Rolle's theorem for c=2+ 1 3 , then
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