Application of Derivatives questions
910 published questions with worked solutions.
- The shortest distance between line y − x = 1 and curve x = y^2 is
- For x (0, 5 2 ), define f(x) = _0^x t t ,dt. Then f has
- The co-ordinates of a point on the curve y=x x at which the normal is parallel to the line 2x-2y=3 are
- The equation of normal to the curve x= + , y=1+ at = 2 is
- The approximate value of [3] 0.026 is
- If Rolle's theorem holds for the function f(x)=x^3+bx^2+ax+5 on [1, 3] with c=2+ 1 3 , then the values of a and b respectively are
- The curve y = ax^3 + bx^2 + cx + 5 touches the x-axis at (-2, 0) and cuts the y-axis at a point Q where its gradient is 3, then...
- If y = a x + bx^2 + x has its extreme value at x = -1 and x = 2, then the value of a + b is
- If f(x) = x^3 + bx^2 + cx + d and 0 < b^2 < c, then in (- , )
- The value of c for which Rolle's theorem for the function f(x) = x^3 - 3x^2 + 2x in the interval [0, 2] are
- The equation of the normal to the curve x= + , y=1+ at = 2 is
- A stone is dropped into a quiet lake and waves move in circles at speed of 8 cm/sec. At the instant when the radius of the...
- The approximate value of ^ -1 (0.999) is (use = 3.1415)
- A ladder 5m long rests against a vertical wall. If its top slides downwards at the rate of 10 cm./sec., then the foot of the...
- The equation of the tangent to the curve y = 1 - e^ x 3 at the point of intersection with Y-axis is
- If f(x) = ( ^4x + ^4x ), 0 < x < 2 , then the function has minimum value _____ at x =
- If sum of two numbers is 3, then the maximum value of the product of first number and square of the second number is
- Given that the slope of the tangent to a curve y=y(x) at any point (x,y) is 2y x^2 . If the curve passes through the centre of...
- A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side x units and a circle of...
- The approximate value of _ 10 1002 is (Given _ 10 e=0.4343)
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