The Function  has A Local Maximum At x =

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Question

The function  has a local maximum at x =

Solution

Correct option is

2

Given, 

            

            

                                                                         (Using Leibnitz rule)

Using number line rule for f’(x) we get fig which shows local maxima at x = 2 as f’(x) changes from (+ve) to (–ve) and local minima at x = 1 and x = 3 as f’(x) changes from (–ve) to (+ve).

∴ Local minima at x = 1, 3 and local maximum at x = 2.

Testing

SIMILAR QUESTIONS

Q1

If (x) and (x) are two positive and increasing function, then

Q2

If the function y = sin (f (x)) is monotonic for all values of x (where (x) is continuous), then the maximum value of the difference between the maximum and the minimum value of (x), is: 

Q3

 where 0 <x < π then the interval in which g(x) is decreasing is:   

Q4

Find the critical points for f (x) = (x – 2)2/3 (2x + 1).

Q5

 

Find all the values of a for which the function possess critical points.

 

Q6

 

Using calculus, find the order relation between x and tan-1x when x Ïµ [0, ∞). 

Q7

Using calculus, find the order relation between x and tan-1x when  

Q8

The set of all values of ‘b’ for which the function (x) = (b2 – 3b + 2) (cos2x – sin2x) + (b – 1) x + sin 2 does not possesses stationary points is:

Q9

 

Find the local maximum and local minimum of (x) = x3 + 3x in [–2, 4].

Q10

Find the set of critical points of the function