Question

# The image of the interval [- 1, 3] under the mapping specified by the function is :

- [f(+1), f(-1)]
- [f(-1), f(3)]
- [- 8, 16]
- [-8, 72]

## The correct answer is: [-8, 72]

### we are asked to find the image of the interval under the mapping specified by the function

we need to differentiate the function to get local maxima/minima

f′(x)=12(x^{2}−1)

f′(x)=0 at x=±1

f′(x)<0 If ∣x∣<1

function will be increasing in this range (∣x∣<1 )

f′(x)>0 If ∣x∣>1

function will be increasing in this range (∣x∣>1 )

f(x) is min when x=1

f(1)=−8

f(x) is max either at x=−1 or x=3

f(−1)=8 , f(3)=72

So image [-8, 72] in [-1, 3]

f′(x)=12(x2−1)

f′(x)=0 at x=±1

f′(x)<0 If ∣x∣<1

f′(x)>0 If ∣x∣>1

f(x) is min when x=1

f(1)=−8

f(x) is max either at x=−1 or x=3

f(−1)=8 , f(3)=72

So image [-8, 72] in [-1, 3]

Hence the correct option in [-8,72]

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