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Derivatives

Derivatives

Derivatives: A Slippery Slope True or False

1. Find the slope of the secant line between the two points shown on the graph of f(x) = cos(x):

 

-> 1

2. Let f(x) = x2 – 1. Find the slope of the secant line between the points (-1, f(-1)) and (2, f(2)).

-> 1

3. Which picture most closely resembles the limit definition of the derivative of f at a? ->


4. The derivative of f(x) = |x – 1| at x = 1 is -> 0
5. Let y = f(x) and assume f ' (a) exists. Which of the following quantities must equal f ' (a)? ->
6. If x is measured in cookies, y is measured in glasses of soda, and z is measured in slices of cake, then  is measured in

-> slices of cake per glass of soda

7. Use the limit definition to find the derivative of f(x) = x2 + x at x = 2.

-> 5 + h


8. Use the following table to estimate the derivative of f at x = 4.

-> 0.25

9. If f(1) = 12 peacocks and f(5) = 36 peacocks, find the average rate of change of f with respect to x on the interval from 1 to 5. The value of x is measured in chocolate bars. -> 6 peacocks per chocolate bar
10. Let f be a function. Which of the following statements is true? -> The slope of f at a is the same thing as the derivative of f at a.

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