Application of Derivatives questions
910 published questions with worked solutions.
- Let f(x) = cases e^x & for 0 x 1 2 - e^ x-1 & for 1 < x 2 x - e & for 2 < x 3 cases and g(x) = _0^x f(t) ,dt, 1 x 3. Then g(x) has
- The length of the longest interval in which the function 3 x - 4 ^3 x is increasing is
- The point(s) on the curve y^3 + 3x^2 = 12y, where the tangent is vertical (i.e., parallel to the y-axis), is/are
- A tangent to the curve y = f(x) at P(x, y) cuts the x-axis and the y-axis at A and B, respectively, such that BP : AP = 3 : 1. If...
- f(x) is a polynomial of the third degree which has a local maximum at x = -1. If f(1) = -1, f(2) = 18 and f'(x) has a local...
- If f(x) is a twice differentiable function such that f(a) = 0, f(b) = 2, f(c) = -1, f(d) = 2 and f(e) = 0, where a < b < c < d <...
- The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c - 1, e^ c-1 ) and (c + 1,...
- Let f(x) = 2 + x for all real x. STATEMENT-1: For each real t, there exists a point c in [t, t + ] such that f'(c) = 0....
- The total number of local maxima and local minima of the function f(x) = cases (2+x)^3, & -3 < x -1 x^ 2/3 , & -1 < x < 2 cases is
- Let the function g : (- , ) (- 2, 2 ) be given by g(u) = 2 ^ -1 (e^u) - 2. Then g is
- Let f(x) be a non-constant twice differentiable function defined on (- , ) such that f(x) = f(1 - x) and f' ( 14 ) = 0. Then,
- For the function f(x) = x 1x, x 1
- Match the statements/expressions given in Column I with the values given in Column II. Column I: (A) The number of solutions of...
- The maximum value of the function f(x) = 2x^3 - 15x^2 + 36x - 48 on the set A = x x^2 + 20 9x is
- Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^ x^2 + e^ -x^2 , g(x) = xe^ x^2 + e^ -x^2 and...
- The maximum value of the expression 1 ^2 + 3 + 5 ^2 is
- Let f be a real-valued differentiable function on R , the set of real numbers, such that f(1) = 1. If the y-intercept of the...
- Let f be a function defined on R , the set of real numbers, such that f'(x) = 2010(x - 2009)(x - 2010)^2(x - 2011)^3(x - 2012)^4...
- The normal to the curve x^2 + 2xy - 3y^2 = 0, at (1, 1)
- Let f(x) be a polynomial of degree four and having its extreme values at x = 1 and x = 2. If _ x 0 [1 + f(x) x^2 ] = 3, then f(2)...
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