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Review of Chapter 3 February 21, 2013
Let f be defined at c. If f '(c)=0 or f is not differentiable at c, then c is a critical number of f.
True or False
T
Review of Chapter 3 February 21, 2013
True or False
x= π is a critical number of f(x)=csc(x)
F
Review of Chapter 3 February 21, 2013
True or FalseThere is a relative maximum or a relative minimum at every critical point
F
Review of Chapter 3 February 21, 2013
True or FalseEvery relative maximum and relative minimum of a function must occur at a critical number or an endpoint
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Review of Chapter 3 February 21, 2013
True or FalseThe maximum of a function that is continuous on a closed interval can occur at two different values in the interval.
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Review of Chapter 3 February 21, 2013
True or False
A function can never have an absolute extreme value on an open interval.
F
Review of Chapter 3 February 21, 2013
True or FalseEvery continuous function must have either an absolute minimum or an absolute maximum on an open interval.
F
Review of Chapter 3 February 21, 2013
True or FalseEvery continuous function must have an absolute minimum or an absolute maximum on a closed interval.
T
Review of Chapter 3 February 21, 2013
True or FalseIf x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x) + k, where k is a constant.
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Review of Chapter 3 February 21, 2013
True or FalseIf x=c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x-k), where k is a constant.
F
Review of Chapter 3 February 21, 2013
True or FalseIf f is continuous and differentiable on the interval [a,b], then if f(a) = f(b) there is at least one number c in (a,b) such that f '(c) = 0
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Review of Chapter 3 February 21, 2013
True or FalseIf f is continuous and differentiable on [a,b], then there exists a c ∈(a,b) such that
f '(c) = f(b) - f(a)b - a
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Review of Chapter 3 February 21, 2013
If f(x) =
True or False
1x then f(1) - f(-1)
1 - (-1)= 1
so f '(c) = 1 for some c∈(-1,1)
F
Review of Chapter 3 February 21, 2013
True or False
If the graph of a function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal.
F
Review of Chapter 3 February 21, 2013
True or False
If the graph of a polynomial function has three x-intercepts, then it must have at least two points at which its tangent line is horizontal.
T
Review of Chapter 3 February 21, 2013
True or False
If f '(x) < 0 for all x∈(0,∞) then f(x) is decreasing for x∈(0,∞)
T
Review of Chapter 3 February 21, 2013
True or FalseIf f '(x) > 0 for all x∈(0,∞) then lim
x→∞f(x) = ∞
F
Review of Chapter 3 February 21, 2013
True or False
Every nth degree polynomial has (n-1) critical numbers
F
Review of Chapter 3 February 21, 2013
True or FalseIf f "(x) > 0 for x∈(a,b), then f(x) is increasing for x∈(a,b)
FIt could be increasing, but it doesn't have to be
Review of Chapter 3 February 21, 2013
True or FalseIf f "(c) = 0, then f has an inflection point at x=c
F
There could be, but there doesn't have to be
Review of Chapter 3 February 21, 2013
True or FalseIf f ' (c) = 0 and f "(c) > 0 then f(c) is a relative maximum
F
Review of Chapter 3 February 21, 2013
True or False
The graph f(x) = 1x has a point of inflection at x=0
F
Review of Chapter 3 February 21, 2013
True or FalseThis is a point of inflection
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Review of Chapter 3 February 21, 2013
True or FalseThis is a point of inflection
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Review of Chapter 3 February 21, 2013
True or FalseThis is a point of inflection
F
Review of Chapter 3 February 21, 2013
True or FalseThere are 2 points of inflection in this graph
F
Review of Chapter 3 February 21, 2013
True or FalseThe absolute maximum of y= 3 sin(x) + 2 cos(x) = 5
F
Review of Chapter 3 February 21, 2013
True or False
The maximum slope of the graph of y = sin(bx) is b
T
-b≤y' = b cos(bx) ≤b
Review of Chapter 3 February 21, 2013
True or False
The graph of f(x) = 4x3 - 2x2x3+ 5
has a horizontal asymptote
T
limx→∞
f(x) = 2
Review of Chapter 3 February 21, 2013
True or False
The graph of f(x) =sin(x)
1 + cos(x) has a vertical asymptote