Application of Derivatives questions
910 published questions with worked solutions.
- Which of the following points lies on the tangent to the curve x^4e^y+2 y+1 =3 at the point (1, 0) ?
- If the lines x + y = a and x – y = b touch the curve y=x^2-3x+2 at the points where the curve intersects the x-axis, then a b is...
- The position of a moving car at time t is given by f(t)=at^2+bt+c, t > 0, where a, b and c are real numbers greater than 1. Then...
- Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10m; then the...
- The set of all real values of for which the function f(x)=(1- ^2x).( + x), x (- 2 , 2 ), has exactly one maxima and exactly one...
- For all twice differentiable functions f : R → R, with f(0) = f(1) = f'(0) = 0
- If the tangent to the curve, y = f(x) = x _ex, (x > 0) at a point (c, f(c)) is parallel to the line - segment joining the points...
- For natural number n, 2^n (n-1)! < n^n, if
- For positive real numbers a, b, c which one of the following holds?
- If 0 < x < 2 , then minimum value of ^3 x x + ^3 x x is
- If a, b, c are different positive real numbers such that (b + c - a), (c + a - b) and (a + b - c) are positive, then (a + b -...
- Consider the following statements: 1. x 1+x^2 < ^ -1 x < x; x > 0 2. If 0 x < 2 , x + x - 3x 0 Which of these is/are correct?
- The minimum value of P = bcx + cay + abz, when xyz = abc, is
- If a + b = 8, then ab is greater when
- If a_i > 0 for i = 1, 2, , n and a_1 a_2 a_n = 1, then minimum value of (1 + a_1)(1 + a_2) (1 + a_n) is
- If ab = 4 (a, b R^+), then
- For any x, y R, xy > 0 then the maximum value of 2x y^3 + x 3y^3 + 4y^2 9x^4 is
- If x, y R^+ satisfying x + y = 3, then the maximum value of x^2 y is
- If x, y and z are positive real numbers and x = 12 - yz y + z . The maximum value (xyz) equals
- For x 0, the smallest value of the function f(x) = 4x^2 + 8x + 13 6(1 + x) , is
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