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Open Response Questions Show all your algebraic steps to support your answer. Include diagrams and sketches where necessary. All answers must be expressed as exact values unless otherwise stated. 11. Given the following analysis of a function, sketch a possible graph for the function. (4 marks) y 10 f(-1) = -2 8 f(5) = 7 $\lim_{x\to 3^{+}} f(x) = -\infty$ 6 $\lim_{x\to 3^{-}} f(x) = \infty$ 4 f'(5) = 0 2 f'(x) < 0 for x > 5 -8 -6 -4 -2 2 4 6 8 x f'(x) > 0 for x < 3 -2 f''(-1) = 0 -4 f''(5) < 0 -6 -8

          Open Response Questions
Show all your algebraic steps to support your answer. Include diagrams and sketches where necessary.
All answers must be expressed as exact values unless otherwise stated.
11. Given the following analysis of a function, sketch a possible graph for the function. (4 marks)
y
10
f(-1) = -2
8
f(5) = 7
$\lim_{x\to 3^{+}} f(x) = -\infty$
6
$\lim_{x\to 3^{-}} f(x) = \infty$
4
f'(5) = 0
2
f'(x) < 0 for x > 5
-8 -6 -4 -2
2 4 6 8 x
f'(x) > 0 for x < 3
-2
f''(-1) = 0
-4
f''(5) < 0
-6
-8

Open Response Questions
Show all your algebraic steps to support your answer. Include diagrams and sketches where necessary.
All answers must be expressed as exact values unless otherwise stated.
11. Given the following analysis of a function, sketch a possible graph for the function. (4 marks)
y
10
f(-1) = -2
8
f(5) = 7
limx→ 3^+ f(x) = -∞
6
limx→ 3^- f(x) = ∞
4
f'(5) = 0
2
f'(x) < 0 for x > 5
-8 -6 -4 -2
2 4 6 8 x
f'(x) > 0 for x < 3
-2
f”(-1) = 0
-4
f”(5) < 0
-6
-8

Added by Diamond M.

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