Correct Answer: Option C

Explanation

f(x) = 3x\(^2\) + 18x + 32

the function will have a least value if f''(x) is greater tan zero ie f'(x)>0 f'(x) = 6x + 18

f''(x) = 6 Since f''(x)>0,

The function has a least value at the turning point, gradient, i.e., f'(x) = 6x + 18 = 0

6x + 18 = 0

6x = -18

x = -\(\frac{18}{6}\)

x = -3

Put x = -3 into f(x) to determine the least value 3(-3)\(^2\) + 18(-3) + 32

3(9) - 54 + 32

27 - 54 + 32 = 5

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