Answer:
a) inc: (-6, 2) ∪ (8, 11); dec: (2, 8)
b) (2, 4) and (8, -2)
c) min: (-8, -3); max: (2, 4)
d) D: [-6, 11]; R: [-3, 4]
e) -2
f) {0, 4}
g) up: (6, 10); down: (0, 6) ∪ (10, 11)
Explanation:
a)
The graph is increasing where the slope is positive. The graph is decreasing where the slope is negative. Points where the slope is zero are not part of the interval. End points of the domain are generally not included, either.
increasing: (-6, 2) ∪ (8, 11)
decreasing: (2, 8)
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b)
Critical points are points where the slope is zero (tangents are horizontal) or undefined (tangents are vertical).
critical points: (2, 4) and (8, -2)
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c)
Minima and maxima are found either at turning points or the ends of the domain. Here, we have ...
absolute minimum: (-8, -3)
local minimum: (8, -2)
local maximum: (11, 1)
absolute maximum: (2, 4)
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d)
The domain is the horizontal extent of the graph. The range is the vertical extent.
domain: [-6, 11]
range: [-3, 4]
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e)
To find the function value for a given value of x, locate that value of x on the graph and see where the function crosses that vertical grid line. Here, the point is marked (8, -2).
f(8) = -2
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f)
Points where f(x) = 3 will have y-coordinates of 3. They will be at the intersection of the horizontal line y=3 and the graph. Here, they are marked for you:
f(0) = 3
f(4) = 3
The values of x where f(x) = 3 are 0 and 4.
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g)
Concavity switches from up to down, or vice versa, at points of inflection. Here, the points of inflection are hard to determine. We will assume they are the points marked (6, 0) and (10, 0).
Where the graph has a ∩ shape (slope is decreasing), the concavity is down. Where the graph has a ∪ shape (slope is increasing), the concavity is up. The slope on the interval (-6, 0) is constant at +1, so is neither increasing nor decreasing. There is no concavity on that interval.
concave down: (0, 6) ∪ (10, 11)
concave up: (6, 10)