# 49. Let f(t) be the temperature at time t where you live and suppose that at time t3 you feeluncomfortably hot. How do you feel about the given data in each case?a. f (3) 2,f"(3) 4Answerb. f (3) 2,f"(3)= -4Answerc. f' (3)2,f" (3) 4Answerd. f (3)2,f (3)4Answer

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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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