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6:13{Use of Tech} Fuel economy Suppose you own a fuel-efficient hybrid automobile with a monitor on the dashboard that displays the mileage and gas consumption. The number of miles you can drive with g gallons of gas remaining in the tank on a particular stretch of highway is given by m(g) = 50g−25.8g²+12.5g³−1.6g⁴, for 0≤g≤4.
a. Graph and interpret the mileage function.
Find an equation of the line tangent to the given curve at a.
y = (x + 5) / (x - 1); a = 3
{Use of Tech} Flow from a tank A cylindrical tank is full at time t=0 when a valve in the bottom of the tank is opened. By Torricelli’s law, the volume of water in the tank after t hours is V=100(200−t)², measured in cubic meters.
a. Graph the volume function. What is the volume of water in the tank before the valve is opened?
City urbanization City planners model the size of their city using the function A(t) = - 1/50t² + 2t +20, for 0 ≤ t ≤ 50, where A is measured in square miles and t is the number of years after 2010.
a. Compute A'(t). What units are associated with this derivative and what does the derivative measure?
Find an equation of the line tangent to the following curves at the given value of x.
y = csc x; x = π/4
The line tangent to the curve y=h(x) at x=4 is y = −3x+14. Find an equation of the line tangent to the following curves at x=4.
y = (x²-3x)h(x)
