Application of Derivatives questions
910 published questions with worked solutions.
- If x = -1 and x = 2 are extreme points of f(x) = |x| + x^2 + x then:
- If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ]0, 1[:
- Consider f(x) = ^ -1 ( 1 + x 1 - x ), x (0, 2 ). A normal to y = f(x) at x = 6 also passes through the point :
- A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of...
- The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point :
- Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq....
- If the curves y^2 = 6x, 9x^2 + by^2 = 16 intersect each other at right angles, then the value of b is :
- Let f(x) = x^2 + 1 x^2 and g(x) = x - 1 x , x R - -1, 0, 1 . If h(x) = f(x) g(x) , then the local minimum value of h(x) is
- Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x^3 - 9x^2 + 12x + 5 in...
- Let P be a point on the parabola, x^2 = 4y. If the distance of P from the centre of the circle x^2 + y^2 + 6x + 8 = 0 is minimum,...
- The shortest distance between the line y = x and the curve y^2 = x - 2 is:
- Let f: [0, 2] R be a twice differentiable function such that f''(x) > 0, for all x ∈ (0, 2). If (x) = f(x) + f(2 - x), then φ is:
- If S_1 and S_2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x^4 + 12x^3 - 36x^2 +...
- The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:
- Let S be the set of all values of x for which the tangent to the curve y = f(x) = x^3 - x^2 - 2x at (x, y) is parallel to the...
- If f(x) is a non-zero polynomial of degree four, having local extreme points at x = −1, 0, 1; then the set S = x R : f(x) = f(0)...
- If the tangent to the curve, y = x^3 + ax - b at the point (1, −5) is perpendicular to the line, −x + y + 4 = 0, then which one...
- A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm^3/min....
- The tangent and normal to the ellipse 3x^2 + 5y^2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the...
- If the tangent to the curve y = x x^2-3 , x R , (x 3), at a point (α, β) ≠ (0, 0) on it is parallel to the line 2x + 6y - 11 = 0,...
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