Application of Derivatives questions
910 published questions with worked solutions.
- If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate...
- Let a, b ∈ R be such that the function f given by f(x) = |x| + bx^2 + ax, x ≠ 0 has extreme values at x = −1 and x = 2. Statement...
- The real number k for which the equation, 2x^3 + 3x + k = 0 has two distinct real roots in [0, 1] belongs to
- If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm^2/s, then the rate of change of its volume...
- Statement-1: The function x^2(e^x + e^ -x ) is increasing for all x > 0. Statement-2: The functions x^2e^x and x^2e^ -x are...
- The maximum area of a right angled triangle with hypotenuse h is :
- If the curves x^2 + y^2 4 = 1 and y^3 = 16x intersect at right angles, then a value of α is :
- The cost of running a bus from A to B is Rs. (av + b/v) where v km/h is the average speed of the bus. When the bus travels at 30...
- A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in cm^2/min.) of the...
- Let f(1) = −2 and f′(x) ≥ 4.2 for 1 ≤ x ≤ 6. The possible value of f(6) lies in the interval :
- If an equation of a tangent to the curve, y − cos(x + f), −1 − 1 ≤ x ≤ 1 + π, is x + 2y = k then k is equal to :
- If f(x) = ( 35 )^x + ( 45 )^x - 1, x R, then the equation f(x) = 0 has :
- If the Rolle's theorem holds for the function f(x) = 2x^3 + ax^2 + bx in the interval [-1, 1] for the point c = 12, then the...
- Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain...
- For the curve y = 3 , x = e^ , 0 , the tangent is parallel to x-axis when θ is:
- If f( ) = vmatrix 1 & & 1 - & 1 & - -1 & & 1 vmatrix and A and B are respectively the maximum and the minimum values of f( ),...
- Let f and g be two differentiable functions on R such that f'(x) > 0 and g'(x) < 0 for all x R. Then for all x :
- If the volume of a spherical ball is increasing at the rate of 4π cc/sec then the rate of increase of its radius (in cm/sec),...
- Consider the function f : (0, ∞) → (−∞, ∞) given by f(x) = x _e(x) - x + 1. Then which one of the following statements is TRUE ?
- If - 2< < 2 then the minimum value of ^3 + ^3 is
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