Question

 

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

Solution

Correct option is

Minimum = –14 & Maximum = 76

 

Given,                  (x) = x3 + 3x   

 which is strictly increasing for all x Ïµ R and thus, increasing for [–2, 4].

Hence, local minimum is (–2) = (–2)3 + 3(–2) = –14    

and local maximum is f (4) = (4)3 + 3(4) = 76.    

SIMILAR QUESTIONS

Q1

If f : R  R, (x) is a differentiable bijective function, then which of the following is true?

Q2

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

Q3

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: 

Q4

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

Q5

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

Q6

 

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

 

Q7

 

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

Q8

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

Q9

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:

Q10

The function  has a local maximum at x =