Question

Find points of local maximum and local minimum of 

Solution

Correct option is

x = 0

Differentiate f (x) w.r.t x to get: 

         

The only critical point is x = 0.

Let us observe the sign change of f’(x) at critical point x = 0. 

Use the following figure to check how sign of f’(x) is changing about x = 0.

 
   

x = 0 is the only point of local minimum as f’(x) changes sign from negative to positive values.

SIMILAR QUESTIONS

Q1

Find the point of local maximum and local minimum of

Q2

Find points of local maximum and local minimum of f(x) = x2 ex.

Q3

Find points of local maximum and local minimum of (x) = x2/3 (2x – 1). 

Q4

Identify the absolute extrema for the following function.  

                      f (x) = x2 on [–1, 2]

Q5

Identify the absolute extrema for the following function.  

                     f (x) = x3   or    [–2, 2]

Q6

Determine the absolute extrema for the following function and interval.

             g(t) = 2t3 + 3t2 – 12t + 4    on    [– 4, 2]  

Q7

Find the local maximum and local minimum values of the function y = xx.

Q8

A window is in the form of a rectangle surmounted by a semi-circle. The total area of window is fixed. What should be the ratio of the areas of the semi-circular part and the rectangular part so that the total perimeter is minimum?   

Q9

A box of constant volume C is to be twice as long as it is wide. The cost per unit area of the material on the top and four sides is three times the cost for bottom. What are the most economical dimensions of the box?