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Chapter 7.2 Applications of the Second
Derivative
Question: You are able to determine where the graph of a
function f is ____________ or ____________. However,
a function can increase like this or like this ,
and similarly, a function can decrease like this or
like this . _____ can you determine which way it is?
Concavity: Let the function y f (x) be
__________________ on an interval (a,b) . Then,
f is concave up on (a,b) if f is __creasing on (a,b) ;
f is concave down on (a,b) if f is __creasing on
(a,b) .
Inflection Point: is the point on the graph of
f where the tangent line __________ and a
______________ in concavity occurs.
Point of Diminishing Return: is the
___________ term for a point of inflection.
It means you get too little out from what you put in. 2
Concavity Test: Suppose f is _________ differentiable
on an open interval (a,b) .
If f (x) 0 for all x in(a,b), then f is concave ____
on (a,b) .
If f (x) 0 for all x in(a,b), then f is concave ____
on (a,b) .
Answer:
1. Find all critical numbers of ____ and all numbers
where f is ______________. Place these numbers on
the real number line. This ______________ the
number line into open intervals.
2. ______________ a number in __________ interval.
3. __________ the __________________ Test to these
numbers to decide if f is concave ________ or
concave ________ on these intervals. 3
Exa

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