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04:57Interpreting Derivative Values
Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The number after t hours is shown in the accompanying figure.
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a. Explain what is meant by the derivative P'(5). What are its units?
Assume that f'(3) = −1, g'(2) = 5, g(2) = 3, and y = f(g(x)). What is y' at x = 2?
In Exercises 9–18, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x.
y = (4 − 3x)⁹
Find y⁽⁴⁾ = d⁴y/dx⁴ if:
a. y = −2 sin x
Differentiability and Continuity on an Interval
Each figure in Exercises 45–50 shows the graph of a function over a closed interval D. At what domain points does the function appear to be
a. differentiable?
Give reasons for your answers.
Computer Explorations
Use a CAS to perform the following steps in Exercises 55–62.
a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation.
xy³ + tan(x + y) = 1, P(π/4, 0)
