Sarthaks Test
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The least value of the function f(x) = x3 – 18x2 + 96x in the interval [0, 9] is :

A. 126 

B. 135 

C 160 

D. 0

1 Answer

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Option : (D)

f(x) = x- 18x+ 96x 

f(x) = 3x- 36x + 96 

f’(x) = 0 

3x2 - 36x + 96 = 0 

x- 12x + 32 = 0 

x2 - 8x - 4x + 32 = 0 

x (x - 8) - 4(x - 8) = 0 

Now we have 

f(0) = 0,

f(4) = 160,

f(9) = 135 

Hence in the given interval least value is f(0) = 0

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