1. 


f'(2) is the slope of the secant line to the curve y = f(x) at the point (2, f(2)). 
2. 


f'(2) is the slope of the tangent line to the curve y = f(x) at the point (2, f(2)). 
3. 


If f'(x) = 0, then the tangent line to the curve y = f(x) at (x, f(x)) is horizontal. 
4. 


If f'(x) 0, then the tangent line to the curve y = f(x) at (x, f(x)) is not horizontal. 
5. 


If f(x) = x^{3}(x^{2 }1), then f'(x) = 3x^{2}(2x 0). 
6. 


If the position s of a particle is given by s = 2t (t = time in seconds), then the particle has a speed of 2 units per second 
7. 


The average velocity of a particle over the time interval [a, b] is given by the slope of the tangent of the position vs. time graph through the point (a, b). 
8. 


The average velocity of a particle over the time interval [a, b] is given by the slope of the secant of the position vs. time graph through the points with time coordinates a and b. 
9. 


The difference quotient of f is the slope of the secant line through the points (x, f(x)) and (x+h, f(x+h)). 
10. 


The derivative is obtained from the difference quotient by setting h=0 
11. 


The difference quotient is the limit of the derivative as h0. 
12. 


If f(x)3 as x4, then f(3) = 4. 
13. 


If  x3^{_}  f(x) = 4,
and 
x3  f(x) exists, then  x3^{+}  f(x) = 4. 

14. 


x3  x^{3}  x
x^{2} + 1  = 
x3  x^{3}
x^{2}  = 
3 

15. 



16. 


If a soccer ball is at rest and s represents its position, then ds/dt = 0. 
17. 


If the marginal revenue is zero at some value of q, then the revenue is increasing rapidly as q increases. 
18. 


If R(q) is a company's annual revenue (in dollars) as a function of the number of items it sells, then R'(1,000) measures the number of items it sells per year at a production level of 1,000. 
19. 


Suppose that H(n) is the height of an individual (in feet) at age n years. If H'(12) = 0.3, this means that the height of the individual is increasing at a rate of 0.3 feet per year on his or her twelfth birthday. 
20. 


If R(q) is a company's revenue (in dollars) as a function of the number of items it sells, then the units of R'(q) are dollars per item. 