Questions from General Calculus


Q: Use the second derivative to show that the graph in Fig.

Use the second derivative to show that the graph in Fig. 4 is always concave up. Figure 4:

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Q: A cigar manufacturer produces x cases of cigars per day at a

A cigar manufacturer produces x cases of cigars per day at a daily cost of 50x(x + 200)/(x + 100) dollars. Show that his cost increases and his average cost decreases as the output x increases.

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Q: (a) Find the first coordinates of the points on the

(a) Find the first coordinates of the points on the graph in Fig. 4 where the tangent line has slope 3. (b) Are there any points on the graph where the tangent line has slope -7? Explain. Figure 4:...

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Q: The graph of f (x) = -1 + (

The graph of f (x) = -1 + (x - 1)2ex is shown in Fig. 5. Find the coordinates of the relative maximum and minimum points. Figure 5:

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Q: (a) Find the point on the graph of y =

(a) Find the point on the graph of y = e-x where the tangent line has slope -2. (b) Plot the graphs of y = e-x and the tangent line in part (a).

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Q: Find the x-intercepts of y = (x - 1

Find the x-intercepts of y = (x - 1)2 ln(x + 1), x > -1.

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Q: Find the coordinates of each relative extreme point of the given function

Find the coordinates of each relative extreme point of the given function, and determine if the point is a relative maximum point or a relative minimum point. f (x) = e-x + 3x

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Q: Find the coordinates of each relative extreme point of the given function

Find the coordinates of each relative extreme point of the given function, and determine if the point is a relative maximum point or a relative minimum point. f (x) = 5x - 2ex

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Q: Solve for t. e0.05t - 4e-0

Solve for t. e0.05t - 4e-0.06t = 0

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Q: Solve for t. 4e0.01t - 3e0.04t

Solve for t. 4e0.01t - 3e0.04t = 0

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