Question

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

Solution

Correct option is

Maximum x = 0 & Minimum x = 1/5

     

Differentiate w.r.t. x to get:

          

Critical points of f (x) are x = 1/5 and x = 0.

Using the following figure, we can determine how sign of f’(x) is changing at x = 0 and x = 1/5.  

From figure

x = 0 is point of local maximum as sign of f’(x) changes from positive to negative and x = 1/5 is point of local minimum.

As sign of f’(x) is changing from negative to positive.

SIMILAR QUESTIONS

Q1

Find points of local maximum and local minimum of 

Q2

Find the point of local maximum and local minimum of

Q3

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

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?  

Q10

Find the maximum surface area of a cylinder that can be inscribed in a given sphere of radius R