Obtain a maximum value of the function f(x) x\(^3\) - 12x + 11
A
-5
B
-2
C
2
D
27
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
f(x) = x\(^3\) - 12x + 11
\(\frac{df(x)}{dx)}\) = 3x\(^2\) - 12 = 0
∴ 3x\(^2\) - 12 = 0 \(\to\) x\(^2\) = 4
x = \(\pm\)2, f(+2) = 8 - 24 + 11 = -15
= f(-2) = (-8) + 24 + 11
= 35 - 8 = 27
∴ maximum value = 27
Source: Myschool Past Questions Archive (Record #31354)