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Second Derivatives and Beyond

Second Derivatives and Beyond

Second Derivatives and Beyond: Thinking Critical True or False

1. A critical point of a function f is a point at which -> ' is zero or undefined
2. Which of the following statements about the function is true? -> x = 0 is the only critical point of f.
3. An inflection point of a function f is a point at which -> " is zero or undefined
4. Which of the following statements about the function f(x) = 4(x – 1) – 8 is true? -> x = 1 is the only inflection point of f.
5. A maximum value of a function f is -> a y-value that is bigger than every nearby value of f.
6. How many minima does the function f(x) = -5cos x have? -> one
7. x = c is a critical point of the function f. The sign of ' is negative to the left of c and positive to the right of c. Which of the following statements is true? -> A minimum value of f occurs at x = c.
8. x = c is a critical point of the function f. If "(c) = 0, which of the following statements is true? -> The second derivative test says nothing at all about what occurs at x = c.
9. If the derivative of a function f is '(x) = (x – 2)(x + 5), which of the following statements is true? -> f has a minimum at x = 2 and a maximum at x = -5.
10. The derivative of the function f is

'(x) = 4x + 8

Which of the following statements is true? -> f has a minimum at x = 2.


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