Find the x-value at which the given function has a point of inflection.

A)
B)
C)
D)
E) no point of inflection

Question

​Find the x-value at which the given function has a point of inflection. ​
​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​no point of inflection

Quizplus · Accepted Answer

A point of inflection occurs when the second derivative changes sign. 
Taking the second derivative of the function yields: 
f''(x) = 24x - 18
Setting this equal to zero gives: 
24x - 18 = 0
Solving for x: 
x = 3/4
Therefore, the point of inflection occurs at x = 3/4, which corresponds to choice C.

​Find the X-Value at Which the Given Function Has a Point

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