Application of Derivatives questions
910 published questions with worked solutions.
- Let f : (0, 1) R be a function defined by f(x) = 1 1-e^ -x , and g(x) = (f(–x) – f(x)). Consider two statements (I) g is an...
- Let x = 2 be a local minima of the function f(x) = 2x^4-18x^2+8x+12, x (–4, 4). If M is local maximum value of the function f in...
- If the equation of the normal to the curve y = x-a (x+b)(x-2) at the point (1, –3) is x – 4y = 13, the value of a + b is equal to...
- Let f : R R be a function such that f(x) = x^2+2x+1 x^2+1 . Then
- If the functions f(x) = x^3 3 +2bx+ ax^2 2 and g(x) x^3 3 +ax+bx^2, a 2b have a common extreme point, then a + 2b + 7 is equal to
- The number of points on the curve y = 54x^5-135x^4-70x^3+180x^2+210x at which the normal lines are parallel to x + 90y + 2 = 0 is
- The absolute minimum value, of the function f(x) = |x^2-x+1|+[x^2-x+1], where [t] denotes the greatest integer function, in the...
- 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 + cos x for all real x. STATEMENT-1 : For each real t, there exists a point c in [t, t + π] such that f′(c) = 0....
- Let the function g : (- , ) (- 2 , 2 ) be given by g(u) = 2 ^ -1 (e^u) - 2 . Then, g is
- For the function f(x) = x 1 x , x 1,
- 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 p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and _ x 0 (1 + p(x) x^2 ) = 2. Then the value of p(2) is
- The maximum distance from origin of a point on the curve x = a t - b ( at b ) y = a t - b ( at b ), both a, b > 0 is
- If the function f(x) = 2x^2 - 9ax^2 + 12a^2x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that...
- The real number x when added to its inverse gives the minimum value of the sum at x equal to
- If u = a^2 ^2 + b^2 ^2 + a^2 ^2 + b^2 ^2 , then the difference between the maximum and minimum values of u^2 is given by
- 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 ' ' always passes through the fixed point
- Area of the greatest rectangle that can be inscribed in the ellipse x^2 a^2 + y^2 b^2 = 1 is
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