1. 


Every absolute maximum is also a local maximum. 
2. 


Every local extremum is also an absolute extremum. 
3. 


Each point of the graph where the tangent is vertical is a singular point. 
4. 


Not all critical points need be local extrema. 
5. 


If we set f'(x) = 0 and obtain the equation x(x^{2} 1) = 0, then we can divide both sides by x to get x^{2} 1 = 0, so that x = ± 1. 
6. 


If a stationary point is not a local extremum, then the tangent at the point need not be horizontal. 
7. 


If f has local maxima at 1 and 2, and if f(1) = 0 and f(2) = 100, then f must have an absolute maximum at 2. 
8. 


Some functions have local extrema but no absolute extrema. 
9. 


If f''(a) is positive, then the graph of f is concave up at x = a. 
10. 


If f'(a) = 0 and f''(a) = 3, then f has a local minimum at x = a. 
11. 


If the graph of f has a point of inflection at x = 3, then f''(3) must be 0 if it is defined. 
12. 


If f''(3) is defined and equals 0, then the graph of f must have a point of inflection at x = 3. 
13. 


If A is a function of time t, and if A = 5 at time t = 2, then dA/dt = 0 at time t = 2. 
14. 


The phrase "A is decreasing at 10 units per second" translates to dA/dt = 10. 
15. 


If r and h vary with time, then  d
dt  (r^{2}h)  =  2rh  dr
dt  . 

16. 


If r and h vary with time, then  d
dt  (r^{2}h)  =  2rh  dr
dt  +  r^{2}  dh
dt 

17. 


If the elasticity of demand E is 2, then an increase in price by 1% will approximately double the revenue. 
18. 


If E = 2, then a 1% increase in price will increase the demand by approximately 2%. 
19. 


If E = 3.2, then a 1% increase in price will decrease the demand by approximately 3.2%. 
20. 


If E = 1, then a 1% decrease in price will increase the demand by approximately 1% 