Application of Derivatives questions
910 published questions with worked solutions.
- Let a_1, a_2, a_3, be an A.P. with a_6 = 2. Then the common difference of this A.P., which maximises the product a_1a_4a_5, is:
- If a right circular cone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm²) of...
- If is one of the angles between the normals to the ellipse, x^2 + 3y^2 = 9 at the points (3 , 3 ) and (-3 , 3 ); (0, 2 ); then 2...
- Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If _ x 0 ( f(x) x^2 + 1 ) = 3 then f(–1) is equal...
- A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is ^ -1 ( 12 ). Water is poured into it...
- Let f(x) = e^x - x and g(x) = x^2 - x, ∀ x ∈ R. Then the set of all x ∈ R, where the function h(x) = (f∘g)(x) is increasing, is:
- The maximum volume (in cu. m) of the right circular cone having slant height 3 m is:
- If θ denotes the acute angle between the curves, y = 10 - x^2 and y = 2 + x^2 at a point of their intersection, then |tan θ| is...
- If m is the minimum value of k for which the function f(x) = x kx - x^2 is increasing in the interval [0, 3] and M is the maximum...
- If the function f given by f(x) = x^3 - 3(a - 2)x^2 + 3ax + 7, for some a ∈ R is increasing in (0, 1] and decreasing in [1, 5),...
- The tangent to the curve y = x^2 - 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point:
- The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 -...
- The maximum value of 3 + 5 ( - 6 ) for any real value of θ is:
- Let f(x) = x a^2 + x^2 - d - x b^2 + (d - x)^2 , x ∈ R, where a, b and d are non-zero real constants. Then:
- Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression x^my^n (1 + x^ 2m )(1 + y^ 2n )...
- The maximum value of the function f(x) = 3x^3 - 18x^2 + 27x - 40 on the set S = x R : x^2 + 30 11x is:
- The tangent to the curve, y = xe^ x^2 passing through the point (1, e) also passes through the point:
- A helicopter is flying along the curve given by y - x^ 3/2 = 7, (x ≥ 0). A soldier positioned at the point ( 12, 7 ) wants to...
- The shortest distance between the point ( 32, 0 ) and the curve y = x, (x > 0), is:
- Let I = _a^b(x^4 - 2x^2) ,dx. If I is minimum then the ordered pair (a, b) is:
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