Exam 13: Additional Differentiation Topics

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Suppose you deposit $1000 in a savings account with 3.6% interest compounded monthly.Then A,the amount of money in the account after t years,is given by A = 1000(1.00 Suppose you deposit $1000 in a savings account with 3.6% interest compounded monthly.Then A,the amount of money in the account after t years,is given by A = 1000(1.00    .Use logarithmic differentiation to find    . .Use logarithmic differentiation to find Suppose you deposit $1000 in a savings account with 3.6% interest compounded monthly.Then A,the amount of money in the account after t years,is given by A = 1000(1.00    .Use logarithmic differentiation to find    . .

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Find y' if y = Find y' if y =    . .

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Differentiate: f(x)= Differentiate: f(x)=

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Use your graphing calculator to graph the equation y = Use your graphing calculator to graph the equation y =    -    - 36    - 29.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results. - Use your graphing calculator to graph the equation y =    -    - 36    - 29.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results. - 36 Use your graphing calculator to graph the equation y =    -    - 36    - 29.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results. - 29.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results.

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Suppose that c = (0.2q - Suppose that c = (0.2q -    + 20,000 is a total cost function,where c is the total cost (in dollars)of producing q units of a product.How fast is marginal cost changing when q = 150? + 20,000 is a total cost function,where c is the total cost (in dollars)of producing q units of a product.How fast is marginal cost changing when q = 150?

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Find y' if y = Find y' if y =    . .

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If y = If y =    ,find    . ,find If y =    ,find    . .

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If y = If y =        ,then find y'' at x = 0. If y =        ,then find y'' at x = 0. ,then find y'' at x = 0.

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The total revenue from the sales of a certain product are given by R(x)= The total revenue from the sales of a certain product are given by R(x)=    .Find the marginal revenue. .Find the marginal revenue.

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If f(x)= 4 If f(x)= 4    + 7    - 5x - 3,find f'''(x). + 7 If f(x)= 4    + 7    - 5x - 3,find f'''(x). - 5x - 3,find f'''(x).

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An approximation of one root of An approximation of one root of    - 6x + 3 = 0 is    = 1.Apply Newton's method twice to find the approximation    . - 6x + 3 = 0 is An approximation of one root of    - 6x + 3 = 0 is    = 1.Apply Newton's method twice to find the approximation    . = 1.Apply Newton's method twice to find the approximation An approximation of one root of    - 6x + 3 = 0 is    = 1.Apply Newton's method twice to find the approximation    . .

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