Application of Derivatives questions
910 published questions with worked solutions.
- The normal to the curve x = a( + ), y = a( - ) at any point ' ' is such that
- A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is...
- Let f be differentiable for all x. If f(1) = -2 and f'(x) 2 for x [1, 6], then
- A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm^3/min....
- If the equation a_nx^n + a_ n-1 x^ n-1 + + a_1x = 0, a_1 0, n 2, has a positive root x = , then the equation na_nx^ n-1 + (n -...
- Angle between the tangents to the curve y = x^2 - 5x + 6 at the points (2, 0) and (3, 0) is
- A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence...
- The function f(x) = x 2 + 2 x has a local minimum at
- If p and q are positive real numbers such that p^2 + q^2 = 1, then the maximum value of (p + q) is
- The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the...
- A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = _ex on the interval [1, 3] is
- The function f(x) = ^ -1 ( x + x) is an increasing function in
- Suppose the cube x^3 - px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
- How many real solutions does the equation x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 have?
- For real x, let f(x) = x^3 + 5x + 1, then
- Given P(x) = x^4 + ax^3 + bx^2 + cx + d such that x = 0 is the only real root of P'(x) = 0. If P(-1) < P(1), then in the interval...
- The shortest distance between the line y - x = 1 and the curve x = y^2 is
- Let f : R R be a continuous function defined by f(x) = 1 e^x + 2e^ -x . Statement-1: f(c) = 13, for some c R. Statement-2: 0 <...
- The equation of the tangent to the curve y = x + 4 x^2 , that is parallel to the x-axis, is
- Let f : R R be defined by f(x) = cases k - 2x, & if x -1 2x + 3, & if x > -1 cases . If f has a local minimum at x = −1, then a...
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