Question
Q1)
----------------------------------------------------------------------------------------------------
Q2)
----------------------------------------------------------------------------------------------------
Q3)
----------------------------------------------------------------------------------------------------
Q4)
For the function graphed in the figure, are the following nonzero quantities positive or negative? (a) f (3) positive negative (b)f'(3) positive negative (c) f"( 3) positive negative Give the signs of the first and second derivatives for the following function. Each derivative is either positive everywhere, zero everywhere, or negative everywhere. (a) f'(x) positive zero negative (b) f"(x) positive zero negative Give the signs of the first and second derivatives for the following function. Each derivative is either positive everywhere, zero everywhere, or negative everywhere. (a) f'(x) positive zero negative (b) f"(x) positive zero negative The table gives the number of passenger cars, C = f(t), in millions, in a country in the year t. (a) Do f'(t) and f"(t) appear to be positive or negative during the period 1975-1990? f'(t) appears to be negative and f"(t) appears to be positive. Both f'(t) and f"(t) appear to be negative. Both f'(t) and f"(t) appear to be positive. Both f'(t) and f"(t) appear to be exactly zero. f'(t) appears to be positive and f"(t) appears to be negative. (b) Do f'(t) and f' ) appear to be positive or negative during the period 1990-2000? f'(t) appears to be positive from 1990 to 2000, and f"(t) appears to be negative from 1990 to 1995 and positive from 1995 to 2000. f'(t) appears to be negative from 1990 to 1995 and positive from 1995 to 2000, and f"(t) appears to be positive from 1990 to 2000. f'(t) appears to be negative from 1990 to 2000, and f"(t) appears to be positive from 1990 to 1995 and negative from 1995 to 2000.f'(t) appears to be positive from 1990 to 2000, and f"(t) appears to be positive from 1990 to 1995 and negative from 1995 to 2000. f'(t) appears to be positive from 1990 to 1995 and negative from 1995 to 2000, and f"(t) appears to be negative from 1990 to 2000. (c) Estimate f'(2005). Using units, interpret your answer in terms of passenger cars.
Explanation / Answer
A1) a) f(3) --- NEGATIVE
b) f'(3) --- POSITIVE (because slope is positive)
c) f''(3) -- POSITIVE (curvature is concave upwards)
A2) a) f'(x) --- NEGATIVE
b) f"(x) -- POSITIVE (curvature is upwards)
A3) a) f'(x) --- POSITIVE
b) f"(x) --- NEGATIVE (curvature is downwards)
A4) a) f'(t) is positive and f"(t) both are POSITIVE
b) between 1990-2000
f'(t) is negative between 1990-1995 and then positive between 1995-2000
while f"(t) is positive between 1990-2000
c) f'(2005) = 136.5 - 133.2 / 5 = 0.66
The number of passenger cars in the US was increasing at the rate of
about 0.66 million cars per year
