Question

7. The points of inflection are found by solving the first derivative equal to zero. 8. When the denominator of a rational function is zero the function will always have a vertical asymptote. 9. To determine the behavior of a function near the vertical asymptotes we use left and right hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test. 11. A function can never cross asymptotes. 12. To determine the end behavior of a function we must check the lim x ? ±?. 13. Sketch a graph of a rational function that satisfies the following conditions [4 Marks] f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x = ± 2 f '(-4) = f '(0) = f '(4) = 0 f '(x) < 0 for x < -4, x > 4 f '(x) > 0 for -4 < x < -2, -2 < x < 0 and 0 < x < 2, 2 < 4 f "(0) = 0 f "(x) > 0 for x < -2, 0 < x < 2 f "(x) < 0 for -2 < x < 0, x > 2

          7. The points of inflection are found by solving the first derivative equal to zero.

8. When the denominator of a rational function is zero the function will always
have a vertical asymptote.

9. To determine the behavior of a function near the vertical asymptotes we use left
and right hand limits.

10. Determining if a local extrema is a maximum or minimum cannot be done
using the second derivative test.

11. A function can never cross asymptotes.

12. To determine the end behavior of a function we must check the lim x ? ±?.

13. Sketch a graph of a rational function that satisfies the following conditions [4 Marks]
f(0) = 0, f(-4) = 2, f(4) = -2
f(x) is undefined for x = ± 2

f '(-4) = f '(0) = f '(4) = 0
f '(x) < 0 for x < -4, x > 4
f '(x) > 0 for -4 < x < -2, -2 < x < 0 and
0 < x < 2, 2 < 4

f "(0) = 0
f "(x) > 0 for x < -2, 0 < x < 2
f "(x) < 0 for -2 < x < 0, x > 2

7. The points of inflection are found by solving the first derivative equal to zero.

8. When the denominator of a rational function is zero the function will always
have a vertical asymptote.

9. To determine the behavior of a function near the vertical asymptotes we use left
and right hand limits.

10. Determining if a local extrema is a maximum or minimum cannot be done
using the second derivative test.

11. A function can never cross asymptotes.

12. To determine the end behavior of a function we must check the lim x ? ±?.

13. Sketch a graph of a rational function that satisfies the following conditions [4 Marks]
f(0) = 0, f(-4) = 2, f(4) = -2
f(x) is undefined for x = ± 2

f '(-4) = f '(0) = f '(4) = 0
f '(x) < 0 for x < -4, x > 4
f '(x) > 0 for -4 < x < -2, -2 < x < 0 and
0 < x < 2, 2 < 4

f "(0) = 0
f "(x) > 0 for x < -2, 0 < x < 2
f "(x) < 0 for -2 < x < 0, x > 2

Added by Shelby D.

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