Application of Derivatives questions
910 published questions with worked solutions.
- Let f : R R be a function defined by f(x) = (x - 3)^ n_ 1 (x - 5)^ n_ 2 , n_ 1 , n_ 2 N. Then, which of the following is NOT true...
- Let f and g be twice differentiable even functions on (−2, 2) such that f(1/4) = 0, f(1/2) = 0, f(1) = 1 and g(3/4) = 0, g(1) =...
- Let f : R R be a function defined by f(x) = _ t x t^ 3 − 3t for x < 2; x^ 2 + 2x - 6 for 2 < x < 3; [x − 3] + 9 for 3 x 5; 2x + 1...
- A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an...
- What is the least value of 25 , cosec ^2x+36 ^2x?
- The minimum distance from the point (4, 2) to y^2=8x is equal to
- What is the minimum value of a^2x+b^2y where xy=c^2?
- Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be defined by f(x) = cases 6x + x 2x + x & if x 0, 7 3 & if x = 0. cases...
- Let g(x) = f(x) + f(1 – x) and f"(x) > 0, x (0, 1). If g is decreasing in the interval (0, ) and increasing in the interval ( ,...
- Let the quadratic curve passing through the point (–1, 0) and touching the line y = x at (1, 1) be y = f(x). Then the x-intercept...
- A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the...
- Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of a^5b^3c^2d is 3750 , then the...
- The number of points, where the curve f(x) = e^ 8x -e^ 6x -3e^ 4x -e^ 2x +1, x cuts x-axis, is equal to
- Let f : [2, 4] R be a differentiable function such that (x _ex)f'(x)+( _ex)f(x)+f(x) 1, x [2, 4] with f(2) = 1 2 and f(4) = 1 2 ....
- If the total maximum value of the function f(x) = ( 3e 2 x )^ ^2x , x (0, 2 ), is k e , then ( k e )^8+ k^8 e^5 +k^8 is equal to
- _ 0 x x-2 x x+ 1 3 3x =
- Let the tangent and normal at the point (3 3,1) on the ellipse x^2 36 + y^2 4 =1 meet the y-axis at the points A and B...
- Consider the triangles with vertices A(2, 1), B(0, 0) and C(t, 4), t [0,4]. If the maximum and the minimum perimeters of such...
- Let a tangent to the curve 9x^2+16y^2=144 intersect the coordinate axes at the points A and B. Then, the minimum length of the...
- Let the function f(x) = 2x^3+(2p-7)x^2+3(2p-9)x-6 have a maxima for some value of x < 0 and a minima for some value of x > 0....
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