Questions from General Calculus


Q: The height of a certain plant, in inches, after t

The height of a certain plant, in inches, after t weeks is f (t) = 1/(.05 + e-0.4t). The graph of f (t) resembles the graph in Fig. 3. Calculate the rate of growth of the plant after 7 weeks. Figure...

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Q: Differentiate the following functions. f (x) = e

Differentiate the following functions. f (x) = e(1+x)3

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Q: Differentiate the functions. y = (x2 + x +

Differentiate the functions. y = (x2 + x + 1)3(x - 1)4

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Q: Find d2y/dx2. y = x√x +

Find d2y/dx2. y = x√x + 1

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Q: The length of a certain weed, in centimeters, after t

The length of a certain weed, in centimeters, after t weeks is f (t) = 6/(.2 + 5e-0.5t). Answer the following questions by reading the graph in Fig. 3. (a) How fast is the weed growing after 10 weeks?...

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Q: Let a and b be positive numbers. A curve whose equation

Let a and b be positive numbers. A curve whose equation is is called a Gompertz growth curve. These curves are used in biology to describe certain types of population growth. Compute the derivative...

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Q: Find dy/dx if

Find dy/dx if

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Q: In a study, a cancerous tumor was found to have a

In a study, a cancerous tumor was found to have a volume of f (t) = 1.8253(1 - 1.6e-0.4196t)3 milliliters after t weeks, with t > 1. (Source: Growth, Development and Aging.) (a) Sketch the graphs of f...

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Q: Let f (t) be the function from Exercise 39 that

Let f (t) be the function from Exercise 39 that gives the height (inches) of a plant at time t (weeks). (a) When is the plant 11 inches tall? (b) When is the plant growing at the rate of 1 inch per we...

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Q: Differentiate the following functions. f (x) = eex

Differentiate the following functions. f (x) = eex

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