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Math Help - 2 calculus problems

  1. #1
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    Exclamation 2 calculus problems

    1) Find the equation of the tangent to f(x)=(2x-1)^3 where x=1

    2) Suppose that for a compant manufacturing calculators, the cost, revenue, and profit equations are given by C=90,000+30x R=300x - (x^2)/30 & P=R-C where the production output in 1 week is x calculators. if production is increasing at a rate of 500 calculators per week, when production output is 6,000 calculators, find the rate of increase (decrease) in: a) cost b) revenue, c) profit.

    Any help would be greatly appreciated.
    Thanks!
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  2. #2
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    Quote Originally Posted by salu34 View Post
    1) Find the equation of the tangent to f(x)=(2x-1)^3 where x=1

    2) Suppose that for a compant manufacturing calculators, the cost, revenue, and profit equations are given by C=90,000+30x R=300x - (x^2)/30 & P=R-C where the production output in 1 week is x calculators. if production is increasing at a rate of 500 calculators per week, when production output is 6,000 calculators, find the rate of increase (decrease) in: a) cost b) revenue, c) profit.

    Any help would be greatly appreciated.
    Thanks!
    I'll help you with the first question...

    Find the derivative of f(x):

    f'(x)=6(2x-1)^2

    The slope is the rate of change at a given point, (i.e. it's derivative).

    f'(1)=6

    Now, what is the y-coordinate for x=1?

    f(1)=1

    Use the slope-intercept form for a line:

    y=mx+b

    Plug and chug...

    1=6(1)+b
    b=-5

    y=6x-5
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  3. #3
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    ?

    how did you find that the derivative of 6(2x-1)^2 was 6?
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  4. #4
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    Quote Originally Posted by salu34 View Post
    how did you find that the derivative of 6(2x-1)^2 was 6?
    colby2152 substituted x=1 into the differentiated function.

    f'(1) = 6(2x-1)^2
    f'(1) = 6(2(1)-1)^2
    f'(1) = 6(2-1)^2
    f'(1) = 6(1)^2
    f'(1) = 6
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