Use the following to answer questions :
A cubic graph is shown. Assume required features have integer values.
f(x) = x 3 + 3x 2 - x - 3 (Gridlines are spaced one unit apart.)
-Give the location of the point of inflection.
A) (0, -3)
B) (-3, 3)
C) (-1, 0)
D) (1, -1)

Question

Use the following to answer questions :
A cubic graph is shown. Assume required features have integer values.
f(x) = x 3 + 3x 2 - x - 3  (Gridlines are spaced one unit apart.)
-Give the location of the point of inflection.
A) (0, -3) 
B) (-3, 3) 
C) (-1, 0) 
D) (1, -1)

Quizplus · Accepted Answer

To find the point of inflection, we need to find the second derivative of the function and set it equal to zero. The second derivative of the function is: f''(x) = 6³xS1S1 - 2 Setting f''(x) equal to zero, we get: 6³xS1S1 - 2 = 0 6³xS1S1 = 2 x = 1/3 Therefore, the point of inflection is at (1/3, f(1/3)). Plugging in x=1/3 into the original function, we get: f(1/3) = -13/27 So the answer is (C), (-1/3, -13/27).

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