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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 5

Lesson 10: Connecting a function, its first derivative, and its second derivative

Calculus-based justification for function increasing
Justification using first derivative
Justification using first derivative
Justification using first derivative
Inflection points from graphs of function & derivatives
Justification using second derivative: inflection point
Justification using second derivative: maximum point
Justification using second derivative
Justification using second derivative
Connecting f, f', and f'' graphically
Connecting f, f', and f'' graphically (another example)
Connecting f, f', and f'' graphically

Connecting f, f', and f'' graphically

Let g be a twice differentiable function. One of these graphs is the graph of g, one is of g, prime and one is of g, start superscript, prime, prime, end superscript.

Choose the option that matches each function with its appropriate graph.

(Choice A)
start text, A, end text g g, prime g, start superscript, prime, prime, end superscript
I I, I I, I, I
(Choice B)
start text, B, end text g g, prime g, start superscript, prime, prime, end superscript
I I, I, I I, I
(Choice C)
start text, C, end text g g, prime g, start superscript, prime, prime, end superscript
I, I I, I, I I
(Choice D)
start text, D, end text g g, prime g, start superscript, prime, prime, end superscript
I, I, I I I, I

start text, A, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I	I, I	I, I, I

start text, A, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I	I, I	I, I, I

start text, B, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I	I, I, I	I, I

start text, B, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I	I, I, I	I, I

start text, C, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I, I	I, I, I	I

start text, C, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I, I	I, I, I	I

start text, D, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I, I, I	I	I, I

start text, D, end text	g	g, prime	g, start superscript, prime, prime, end superscript
	I, I, I	I	I, I

Stuck?

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 5

Problem