Question
Asked Oct 29, 2019
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49. 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
Answer
b. f (3) 2,
f"(3)= -4
Answer
c. f' (3)2,
f" (3) 4
Answer
d. f (3)2,
f (3)4
Answer
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49. 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 Answer b. f (3) 2, f"(3)= -4 Answer c. f' (3)2, f" (3) 4 Answer d. f (3)2, f (3)4 Answer

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Expert Answer

Step 1

a) f'(3)=2, f"(3)=4

f'(3) > 0 , so the temperature f(t) is  increasing at x=3

f"(3)>0 implies at x=3, f(x) is concave up so rate of change is increasing. 

Answer(a): f(x) is increasing and concave up at x=3

Step 2

b) f'(3)=2, f"(3)= -4

f'(3) > 0 , so the temperature f(t) is  increasing at x=3.

f"(3)<0 implies at x=3, f(x) is concave down so rate of change is decreasing. 

Answer(b): f(x) is increasing and concave down at x=3

Step 3

c) f'(3)= -2, f"(3)= 4

f'(3) < 0 , so the temperature f(t) is  decreasing at x=3.

f"(3)>0 implies at x=3, f(x) is concave...

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