MTH 251 Differential Calculus Assignment
Product and Quotient Rules
1. Find the derivatives of the following functions.
2.Find the derivative of f (x)and then determine the equation of the tangent line to f at x = 0.
Rates of Change
1. The atmospheric CO2 level A(t) at Mauna Loa, hawaii, at time t (in parts per million by volume) is recorded by the Scripps Institution of Oceanography. Reading across, the values for the 4-year intervals are
Estimate A ' (t) in 1962, 1970, 1986, and 2002. In which of the years did the approximation take on its largest and smallest values? In which of these years does the approximation suggest that the CO2 level was the most constant?
2. The dollar cost of producing x video cameras is C(x) = 500x ? 0.003x 2 + 10?8 x 3 . Estimate the marginal cost at production level x = 5000 and compare it with the actual marginal cost C(5001) ? C(5000). Compare this marginal cost with the average cost per camera, defined as C(x)/x.
3. A particle moving along a line has position s(t) = t 4 ? 18t 2 meters at time t seconds. At which times does the particle pass through the origin? At which times is the particle instantaneously motionless (zero velocity
- Higher Derivatives
1. Find a general formula for f (n) (x) if f (x) = x 2 e x .
2. Find the acceleration at time t = 5 min of a helicopter whose height is s(t) = 300t ? 4t 3 meters. Plot the acceleration s 00 for 0 ? t ? 6. Is the helicopter speeding up or slowing down during this time interval? Explain