Exam 3: Shortcuts to Differentiation

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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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Over which of the following intervals is the function Over which of the following intervals is the function   increasing? increasing?

(Multiple Choice)
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Given Given   , find   . , find Given   , find   . .

(Short Answer)
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What is What is   ? ?

(Multiple Choice)
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The equation of the tangent line to the curve The equation of the tangent line to the curve   at the point where it touches the y-axis is y = _____x + _____. at the point where it touches the y-axis is y = _____x + _____.

(Short Answer)
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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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A college savings account is opened the day baby Brad is born. The initial amount deposited is $2500. The account is compounded quarterly at a nominal rate of 3 %. Assuming no other money is deposited in the account, find A(18) and also A'(18).

(Short Answer)
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Consider the function Consider the function   , where a and b are constants. Find   . , where a and b are constants. Find Consider the function   , where a and b are constants. Find   . .

(Short Answer)
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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

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The curve The curve   has a horizontal tangent at which of the following points? Select all that apply. has a horizontal tangent at which of the following points? Select all that apply.

(Multiple Choice)
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The price in dollars of a house during a period of mild inflation is described by the formula The price in dollars of a house during a period of mild inflation is described by the formula   , where t is the number of years after 1990. How many years will it take for the house to triple in value? Round to the nearest year. , where t is the number of years after 1990. How many years will it take for the house to triple in value? Round to the nearest year.

(Short Answer)
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Find the derivative of Find the derivative of   . .

(Multiple Choice)
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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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Consider the function Consider the function   , where a and b are constants. Find   . , where a and b are constants. Find Consider the function   , where a and b are constants. Find   . .

(Short Answer)
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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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Find Find   for   . for Find   for   . .

(Multiple Choice)
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Find the derivative of Find the derivative of   . .

(Multiple Choice)
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