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AP®︎ Calculus BC (2017 edition)

Course: AP®︎ Calculus BC (2017 edition) > Unit 6

Lesson 7: Justifying properties of functions using the second derivative

Inflection points from graphs of function & derivatives
Justification using second derivative: maximum point
Justification using second derivative: inflection point
Justification using second derivative
Justification using second derivative
Worked example: Inflection points from first derivative
Worked example: Inflection points from second derivative
Inflection points from graphs of first & second derivatives
Second derivative test
Second derivative test

Second derivative test

Let g be a twice differentiable function, and let g, left parenthesis, minus, 1, right parenthesis, equals, 4, g, prime, left parenthesis, minus, 1, right parenthesis, equals, 0, and g, start superscript, prime, prime, end superscript, left parenthesis, minus, 1, right parenthesis, equals, 3.

What occurs in the graph of g at the point left parenthesis, minus, 1, comma, 4, right parenthesis?

(Choice A)
left parenthesis, minus, 1, comma, 4, right parenthesis is a minimum point.
(Choice B)
left parenthesis, minus, 1, comma, 4, right parenthesis is a maximum point.
(Choice C)
There's not enough information to tell.

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AP®︎ Calculus BC (2017 edition)

Course: AP®︎ Calculus BC (2017 edition) > Unit 6

Problem