Application of Derivatives questions
910 published questions with worked solutions.
- The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is
- If Rolle's theorem holds for the function x^3+ax^2+bx, 1 x 2 at the point 43, then the values of a and b are respectively.
- If x and y are sides of two square such that y = x - x^2 then the rate of change of area of the second square with respect to...
- The function f(x) = [x(x - 2)]^2 is increasing in the set
- The minimum value of ax + by where xy = c^2 is
- The equation of the tangent to the curve y = be^ -x/a at the point where it crosses the Y axis is
- A manufacturer sells x items at a price of rupees (6- x 40 ) each. The cost price of x items is Rs. ( x5+193 ). The maximum...
- The equation of the tangent to the curve (1+x^2)y=2-x, where it crosses the X-axis, is
- If y= x+ x^3-x has extreme values at x = -1 and x = 1, then and are respectively
- The minimum value of the slope of the tangent to curve y=x^3-3x^2+2x+93 is
- A spherical balloon is filled with 4500 cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate...
- Let f(x) = sin x, g(x) = x. Statement 1: f(x) g(x) for x in (0, ) Statement 2: f(x) 1 for x in (0, ) but g(x) as x .
- If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of 6 cm^2/hr, then the rate...
- If f(x) = xe^ x(1 - x) , x ∈ R, then f(x) is
- Consider a quadratic equation ax^2 + bx + c = 0, where 2a + 3b + 6c = 0 and let g(x) = a x^3 3 + b x^2 2 + cx. Statement 1: The...
- The equation of the normal to the parabola, x^2 = 8y at x = 4 is
- The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish....
- The chord PQ of the parabola y^2 = x, where one end P of the chord is at point (4, −2), is perpendicular to the axis of the...
- The normal at (2, 32 ) to the ellipse, x^2 16 + y^2 3 = 1 touches a parabola, whose equation is
- Let f : (−∞, ∞) → (−∞, ∞) be defined by f(x) = x^3 + 1 Statement 1: The function f has a local extremum at x = 0 Statement 2: The...
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