   Chapter 3.3, Problem 56E

Chapter
Section
Textbook Problem

# Let f ( t ) be the temperature at time t where you live and suppose that at time t = 3 you feel uncomfortably hot. How do you feel about the given data in each case?(a) f ′ ( 3 ) = 2 ,    f ′ ′ ( 3 ) = 4 (b) f ′ ( 3 ) = 2 ,    f ′ ′ ( 3 ) = − 4 (c) f ′ ( 3 ) = − 2 ,    f ′ ′ ( 3 ) = 4 (d) f ′ ( 3 ) = − 2 ,    f ′ ′ ( 3 ) = − 4

To determine

(a)

To write:

How it feels when temperature ft changes with time t

Explanation

1) Concept:

Use the concavity test and given conditions, graph the function and explain the condition

2) Tests:

i. Increasing / Decreasing Test:

If f'x>0 on an interval, then f is increasing on that interval.

If f'x<0 on an interval, then f is decreasing on that interval.

ii. Concavity test:

If f"(x)>0 for all x in I, then the graph of f is concave upward on I

If f"(x)<0 for all x in I, then the graph of f is concave downward on I

3) Given:

f'3=2 and f"(3)=4

4) Calculation:

Suppose at time t=3 it feels uncomfortably hot

To determine

(b)

To write:

How it feels when temperature ft changes with time t

To determine

(c)

To write:

How it feels when temperature ft changes with time t

To determine

(d)

To write:

How it feels when temperature ft changes with time t

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