The points of the curve y = x3 + x - 2 at which its tangent are parallel to the straight line y = 4x - 1 are
(2, 7), (- 2, - 11)
(0, 2), (21/3, 21/3)
(- 21/3, - 21/3), (0, - 4)
(1, 0), (- 1, - 4)
The equation of the normal to the curve y = - + 2 at the point of its intersection with the bisector of the first quadrant is
4x - y + 16 = 0
4x - y = 16
2x - y - 1 = 0
2x - y + 1 = 0
Let the equation ofa curve is given in implicit form as y = . Then in terms of y is
C.
The function f(x) = , f(0) = 0 is
differentiable at x = 0
neither continuous at x = 0 nor differentiable at x = 0
not continuous at x = 0
continuous at x = 0 but not differentiable at x = 0
The values of a and b for which the function y = aloge(x ) + bx2 + x, has extremum at the points x1 = 1 and x2 = 2 are
The tangent to the graph of a continuous function y = f(x) at the point with abscissa x = a forms with the X-axis an angle of and at the point with abscissa x = b an angle of , then what the value of integral
(where f'(x) the derivative off w.r.t. xwhich is assumed to be continuous and similarly f"(x) the double derivative of f w.r.t. x)
eb +
A closed figure S is bounded by the hyperbola x2 - y2 = a2 and the straight line x = a + h; (h > 0, a > 0). This closed figure is rotated about the X-axis. Then, the volume of the solid ofrevolution is