Application of Derivatives questions
910 published questions with worked solutions.
- The number of distinct real roots of the equation x^ 7 - 7x - 2 = 0 is
- Let * be the largest value of for which the function f _ (x) = 4 x^ 3 - 36 x^ 2 + 36x + 48 is increasing for all x ℝ. Then f _ *...
- The line which is parallel to x-axis and crosses the curve y= x at an angle 45^ , is
- The points (x,y) lies on the line 2x+3y=6. Smallest value of the quantity x^2+y^2 is m then the value of 13 m is
- The sum of the maximum and minimum values of the function f(x) = |5x − 7| + [x^ 2 + 2x] in the interval [5/4, 2], where [t] is...
- Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x^ 3 - 3xy^ 2 + 6x^ 2 - 5xy - 8y^ 2 + 9x + 14...
- If the absolute maximum value of the function f(x) = (x^ 2 - 2x + 7)e^ (4x^ 3 - 12x^ 2 - 180x + 31) in the interval [−3, 0] is f(...
- The curve y(x) = ax^ 3 + bx^ 2 + cx + 5 touches the x-axis at the point P(−2, 0) and cuts the y-axis at the point Q, where y' is...
- The slope of the tangent to a curve C : y = y(x) at any point (x, y) on it is (2e^ 2x - 6e^ -x + 9)/(2 + 9e^ -2x ). If C passes...
- Water is being filled at the rate of 1 cm^ 3 / in a right circular conical vessel (vertex downwards) of height 35 cm and diameter...
- If the angle made by the tangent at the point (x_ 0 , y_ 0 ) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)^ 2 , 0 < t <...
- If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x - x^ 2 at the point P and V is the vertex of the parabola,...
- Let f(x) = |(x − 1)(x^ 2 - 2x − 3)| + x − 3, x ℝ. If m and M are respectively the number of points of local minimum and local...
- Let f : ℝ ℝ and g : ℝ ℝ be two functions defined by f(x) = _ e (x^ 2 + 1) - e^ -x + 1 and g(x) = (1 - 2e^ 2x )/e^ x . Then, for...
- Let P and Q be any points on the curves (x - 1)^ 2 + (y + 1)^ 2 = 1 and y = x^ 2 , respectively. The distance between P and Q is...
- If the maximum value of a, for which the function f_a(x) = ^ -1 2x - 3ax + 7 is non-decreasing in (- /6, /6), is ā, then f _ā(...
- Let f(x) = x^ 3 - x^ 2 + 10x - 7 for x 1 and f(x) = −2x + _ 2 (b^ 2 - 4) for x > 1. Then the set of all values of b, for which...
- Let the function f(x) = 2x^ 2 − log_e x, x > 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y^ 2...
- The normal to the hyperbola x^ 2 /a^ 2 - y^ 2 /9 = 1 at the point (8, 3 3 ) on it passes through the point :
- The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x − x^ 2 + 2| − x in the interval [−1,...
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