 ## True/False Quizzes for Applied Calculus Topic: Applications of the Derivative (Chapter 5) Chapter 4 quiz
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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(x2 1) = 0, then we can divide both sides by x to get x2 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 ( r2h) = 2 rh dr dt .
16.
 If r and h vary with time, then d dt ( r2h) = 2 rh dr dt + r2 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% Last Updated: August, 1999