Question

The critical points of the function f (x) where 

Solution

Correct option is

0 , 2, 4

Critical points  

             

   

Clearly       

So       x = 4 is a critical point   

           x = 2 is also a critical point   

because f’(x) is not defined at x = 2    

And x = 0 is a critical  point as f (x) is discontinuous at x = 0.

 

SIMILAR QUESTIONS

Q1

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

Q2

The distance between the origin and the normal to the curve

y = e2x + x2 at x = 0 is

Q3

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

Q4

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

Q5

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

Q6

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 

                          

Q7

The equations of the tangents to the curve y = x4 from the point (2, 0) not on the curve, are given by

Q8

The value of parameter a so that line (3 – ax + ay + (a2n – 1) = 0 is normal to the curve xy = 1, may lie in the interval

Q9

A cylindrical gas container is closed at the top and open at the bottom; if the iron plate forming the cylindrical sides. The ratio of the height to diameter of the diameter of the cylindrical using minimum material for the same capacity is

Q10

Find the abscissa of the point on the curve ay2 = x3, the normal at which cuts of equal intercept from the axes.