Question
In: Math
Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function...
Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function is differentiable everywhere. (III) If f(x) is differentiable everywhere, with f(−1) < 0, and f(2) > 0, then the equation f(x) = 0 must have a solution in the open interval (−1, 2). Which of the following is true?
(a) Only (II) is always true.
(b) Only (I) and (III) are always true.
(c) Only (II) and (III) are always true.
(d) Only (III) is always true.
(e) Only (I) is always true.
A rectangular box with square base and no top is manufactured using sheets of cardboard. The boxes will be used to store 50 cubic inches of tiny pellets that are ready for shipping. The manufacturing company intends to avoid wasting material so it is important to determine the optimal design. Let x be the length of the sides of the base given in inches. Let y be the height of the box given in inches. Which mathematical model is appropriate?
(a) Minimize 2x 2 + 4xy when 2x 2 y = 50.
(b) Minimize 2x 2 y when x 2 + 4xy = 50.
(c) Minimize 2x 2 y when 2x 2 + 4xy = 50.
(d) Minimize x 2 + 4xy when 2x 2 y = 50.
(e) None of the above.
Solutions
milcah answered 2 years agoRelated Solutions
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
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If the production function has strictly isoquants and is differentiable, then there will always be an...
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(a) The units of f ' are
the units of
f
the units of
x
(the units of f)(the units of x
)
the units of f
the units of x
the units of f
(the units of x)2
the units of f
(the units...
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Let f be a continuous function on [a, b] which is differentiable
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can you please prove this theorem? thank you!
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Rolle's Theorem, "Let f be a continuous function on [a,b] that
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Rolle's Theorem requires three conditions be satisified.
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Each...
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