Questions from General Calculus

Q: The graph (from the US Department of Energy) shows how

The graph (from the US Department of Energy) shows how driving speed affects gas mileage. Fuel economy F is measured in miles per gallon and speed v is measured in miles per hour. a. What is the mean...

Q: The graph shows how the average age of first marriage of Japanese

The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch the graph of the derivative function M’(t). During which yea...

Q: The point P(0.5, 0) lies on

The point P(0.5, 0) lies on the curve y = cosπx. a. If Q is the point (x, cosπx), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following value...

Q: Determine the infinite limit. /

Determine the infinite limit.

Q: Make a careful sketch of the graph of f and below it

Make a careful sketch of the graph of f and below it sketch the graph of f’ in the same manner as in Exercises 4–11. Can you guess a formula for f’(x) from its graph? f(x) = ex

Q: Make a careful sketch of the graph of f and below it

Make a careful sketch of the graph of f and below it sketch the graph of f’ in the same manner as in Exercises 4–11. Can you guess a formula for f’(x) from its graph? F(x) = ln x

Q: Let f(x) = x2. a. Estimate

Let f(x) = x2. a. Estimate the values of f’(0), f’(1/2), f’(1), and f’(2) by using a graphing device to zoom in on the graph off. b. Use symmetry to deduce the values of f’(-1 2), f’(-1), and f’(-2)...

Q: Let f(x) = x3. a. Estimate

Let f(x) = x3. a. Estimate the values of f’(0), f’(1/2), f’(1), f’(2), and f’(3) by using a graphing device to zoom in on the graph of f. b. Use symmetry to deduce the values of f’(-1/2), f’(-1), f’(...

Q: Find the derivative of the function using the definition of derivative.

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. f(x) = 3x - 8

Q: Find the derivative of the function using the definition of derivative.

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. f(x) = mx + b