Question

The image of the interval [–1, 3] under the maping f(x) = 4x3 – 12x is.

Solution

Correct option is

[8, 72]

To find the image of the given interval, we must find the set of value of f (x) for x ∈ [–1, 3]. By virtue of the continuity of f (x), the image is the interval

                          

The critical points of f (x) are given by f ‘ (x) = 12 x 2 – 12 = 12(x 2 – 1) = 0.

That is, x = ±1, so that f (1) = 4. 1 – 12 = –8, f (–1)

               = –4 + 12 = 8 and f (3) = 4.  27 – 12. 3 = 108 – 36 = 72.

                   

                  

Hence the image of [–1, 3] under the mapping f (x) is [–8, 72].

SIMILAR QUESTIONS

Q1
Q2

The length of a longest interval in which the function 3 sin x – 4Sin3x is increasing is

Q4

The equation e 1 + x – 2 = 0 as 

Q5

The function f satisfying 

Q6

Suppose f is differentiable on R and a ≤ f’(x) ≤ b for all x ∈ R where ab> 0. If f (0) = 0, then

Q7

The minimum value of (x) = 

Q8

, for every real number, then minimum value of f

Q9

The difference between the greatest and least values of the function 

Q10

 and x = 2, then