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Mathematics
11th -
12thgrade
Graphs of f, f', f'' and using the 1st and 2nd derivative
18 questions
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- 1. Multiple ChoiceThe rate of change of a function is described by its ____________.first derivativesecond derivativethird derivativeexpression
- 2. Multiple ChoiceThe concavity of a function is described by its _______________.first derivativesecond derivativethird derivativeexpression
- 3. Multiple Choice
Suppose a function f is defined so that
f '(x) = x3 - x2 and f "(x) = 3x2 - 2x .
Over what intervals is the graph of f increasing and concave up?x < 00 < x < ⅔⅔ < x < 1x > 1 - 4. Multiple Choice
For a continuous function g(x), g''(3)= -8 indicates that g(x) is ____________ on an interval containing x=3.
increasing
decreasing
concave up
concave down
- 5. Multiple Choice
For a continuous function f(x), f '(-3) = 5 indicates f(x) is ___________ on an interval containing x= -3.
increasing
decreasing
concave up
concave down
- 6. Multiple Choice
If (a,b) is a local maximum and f '(a) = 0, then what will be true about f ''(a)?
f "(a) > 0
f "(a) < 0
f "(a)= 0
Cannot be determined
- 7. Multiple Choice
If (a,b) is a local minimum and f '(a) = 0, then what will be true about f ''(a)?
f "(a) > 0
f "(a) < 0
f "(a) = 0
Cannot be determined
- 8. Multiple Choice
If f '(3) = 0 and f "(3) < 0, then which of the following must be true?
f(x) has a local max at x = 3
f(x) has a local min at x = 3
f(x) has an inflection point at x = 3
f(x) has an x-intercept at x = 3
- 9. Multiple Choice
At what x values does f(x) = x4 - 8x2 have a relative minimum?
0 and -2
0 and 2
-2 and 2
-2, 0, 2
- 10. Multiple Choice
The graph of f '(x) is given. Over what interval(s) is f(x) increasing?
(-∞, -3] ∪ [1, ∞)
[-3, 1]
[-5, 0] ∪ [2, ∞)
[-5, ∞)
- 11. Multiple Choice
The graph of f '(x) is given. At what x-value(s) does f(x) have a minimum? Assume the graph extends infinitely in either direction.
x = -3
x = 1
x = 5
x = -3 and x = 5
- 12. Multiple Choice
The graph of f '(x) is given. On what interval is f decreasing?
[-5,-1] U [3,4]
[-3,1]
[-1,3] U [4,5]
[-5,-3] U [1,5]
- 13. Multiple Choice
The graph of f '(x) is given. On what interval is f increasing?
[-5,-1] U [3,4][-3,1][-1,3] U [4,5]x = -3 and x = 1 - 14. Multiple Choice
The graph of f '(x) is given. For what x-value(s) does f have a relative minimum?
x = -5
x = -3
x = 1
x = 3
x = 5
- 15. Multiple Choice
The graph of f '(x) is given. Identify the interval where f is concave up.
(-1,1) & (3,4)
(-3,-2)
(-2,-1)
(-3,-1) & (1,3)
- 16. Multiple Choice
The graph of f '(x) is given. Identify the interval where f is concave down.
(-1,1) & (3,4)(-2,4)(-3,-1) & (1,3)(-2,1) & (1,4) - 17. Multiple Choice
The graph of f ''(x) is given. Which x values are inflection points of f(x)?
x = -5
x = -3
x = 4
x = -1
- 18. Multiple ChoiceCalc ok. The number of inflection points for the graph of f(x) = 2x + cos(x2) in the interval [0,5] is6789
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