Application of Derivatives questions
910 published questions with worked solutions.
- The parabolas x^ 2 = 5 - 4y and y = x^ 2 cut at the point (1, 1) at an angle
- The number of tangents to the curve y^ 2 - 2x^ 3 - 4y + 8 = 0 that pass through (1, 2) is
- The equation of the tangent to the curve y = e^ -|x| at the point where the curve cuts the line x = 1 is
- The equation of the tangent to the curve y = be^ -x/a where it cuts the y-axis is
- If the tangent to the curve x + y = a at any point on it cuts the axes OX and OY at P and Q respectively then OP + OQ is
- If the line joining the points (0, 3) and (5, -2) is a tangent to the curve y = c x+1 then the value of c is
- The curve x^ n a^ n + y^ n b^ n = 2 touches the line x a + y b = 2 at the point
- The sum of the intercepts made on the axes of coordinates by any tangent to the curve x + y = 2 is equal to
- The area bounded by the axes of reference and the normal to y = _e x at the point (1, 0) is
- The normal to the curve 2x^ 2 + y^ 2 = 12 at the point (2, 2) cuts the curve again at
- Two cyclists start from the junction of two perpendicular roads, their velocities being 3v metres/minute and 4v metres/minute....
- On the curve x^ 3 = 12y the abscissa changes at a faster rate than the ordinate. Then x belongs to the interval
- A balloon is pumped at the rate of a cm³/minute. The rate of increase of its surface area when the radius is b cm, is
- x and y are the sides of two squares such that y = x - x^ 2 . The rate of change of the area of the second square with respect to...
- Let the equation of a curve be x = a( + ), y = a(1 - ). If changes at a constant rate k then the rate of change of the slope of...
- A tangent to the curve y = _ 0 ^ x |t| ,dt, which is parallel to the line y = x, cuts off an intercept from the y-axis equal to
- If xy = a^2 and S = b^2x + c^2y where a, b and c are constants then the minimum value of S is
- The global minimum value of f(x) = x^4 - x^2 - 2x + 6 is
- The maximum value of f(x) = 3 ^2x + 4 ^2x + x 2 + x 2 is
- If a > b > 0, the minimum value of a - b is
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