Application of Derivatives questions
910 published questions with worked solutions.
- STATEMENT-1: The cubic equation 4x^3 - 15x^2 + 14x - 5 = 0 has a root in the interval (2, 3). STATEMENT-2: If f(x) = 0 is a...
- If f(x) is a monotonic increasing function and a R then
- The slope of the tangent to the curve x = y at the point y = ^ -1 (-2) is
- The number of tangents to the curve y = e^ |x| at the point (0, 1) is
- The function f(x) = ax^3 - 3x^2 - 12x + 1 is monotonic decreasing in the open interval (-1, 2). Then one value of a is
- One or more may match with the same. Column I: (i) If f(x) = x + x and g(x) = x^2 - 1 then g f(x) is invertible in the domain...
- If the polynomial function f(x) = ax^3 + bx^2 + cx + d has extrema at x = and x = 2 then
- If f(x) = a^2 ^2 x + b^2 ^2 x + a^2 ^2 x + b^2 ^2 x then the difference between the maximum and minimum values of f(x) ^2 is...
- A point on the parabola y^2 = 18x at which the ordinate increases at twice the rate of the abscissa is
- The normal to the curve x = a(1 + ), y = a at the point ' ' always passes through the fixed point
- Let 0 < < < 2. STATEMENT-1: > STATEMENT-2: If f''(x) > 0, x_1 > x_2 then f(x_1) > f(x_2).
- For all x (0, 1),
- Let f(x) = e^ x ,(x - 1)(x - 2) , dx. Then f decreases in the interval
- If x + y = k is a normal to the parabola y^2 = 12x then k is
- If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3 4 with the positive x-axis then f'(3) is equal to
- Let f(x) = cases |x| & for 0 < |x| 2 1 & for x = 0. cases Then at x = 0, f has
- Consider the following statements S and R. S: Both x and x are decreasing functions in ( 2 , ). R: If a differentiable function...
- More than one may match with the same. Column I: (i) _0^ /2 ( x)^ x x x - ( x)^ x ,dx (ii) The area bounded by -4y^2 = x and x -...
- If f(x) = xe^ x(1-x) then f(x) is
- The triangle formed by the tangent to the curve f(x) = x^2 + bx - b at the point (1, 1) and the coordinate axes, lies in the...
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