The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x2 – x | is


Correct option is

None of these


At and near x = –2  



So the slope of the normal is 1/5 

The options given are wrong.



Consider the parabola y2 = 4xA = (4, –4) and B = (9, 6) be two fixed points on the parabola. Let ‘C’ be moving point on the parabola between A and B such that the area of triangle ABC is maximum, then coordinate of ‘C’ is


If the rate of change of volume of a sphere is the same as rate of change of its radius, then radius, is equal to


A spherical balloon is pumped at the constant rate of 3 m3/min. The rate of increase of its surface area as certain instant is found to be 5 m2/min. At this instant it’s radius is equal to


The third derivative of a function f’’(x) vanishes for all x. If f (0) = 1, f’ (1) = 2 and f’’ = –1, then f (x) is equal to 


The chord joining the points where x = p and x = q on the curve ax2 + bx + c is parallel to the tangent at the point on the curve whose abscissa is 


If the tangent at (1, 1) on y2 = x (2 – x)2 meets the curve again at P, then is


The distance between the origin and the normal to the curve

y = e2x + x2 at x = 0 is


If the line ax + by + c = 0 is a normal to the curve xy = 1 then


The point of intersection of the tangents drawn to the curve x2y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by


The tangent to the graph of the function y = f (x) at the point with abscissax = 1 form an angle of π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle of π/4. The value of