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Math Help - Finding equation of a tangent line given slope of tangent

  1. #1
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    Finding equation of a tangent line given slope of tangent

    This question should be easy but it's giving me some trouble. I am asked to find the equation of the tangent to f(x)=2x^4 and told that the slope of the tangent is 1.

    It is worded exactly: "Find the equation of a the tangent line to the graph f(x)=2x^4 that has slope 1.

    So I found the derivative of f(x) to be f'(x)=8x^3

    I then substituted f'(x) with 1 and found that x=1/2.

    I substituted 1/2 into the original equation for x and found that f(x)= 1/8.

    I then used (y-1/8)=1(x-1/2) and found the equation of the tangent to be y=x-3/8

    The answer in my book was 8x-8y-3=0

    Where did I go wrong?
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  2. #2
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    Quote Originally Posted by Apathy View Post
    This question should be easy but it's giving me some trouble. I am asked to find the equation of the tangent to f(x)=2x^4 and told that the slope of the tangent is 1.

    It is worded exactly: "Find the equation of a the tangent line to the graph f(x)=2x^4 that has slope 1.

    So I found the derivative of f(x) to be f'(x)=8x^3

    I then substituted f'(x) with 1 and found that x=1/2.

    I substituted 1/2 into the original equation for x and found that f(x)= 1/8.

    I then used (y-1/8)=1(x-1/2) and found the equation of the tangent to be y=x-3/8

    The answer in my book was 8x-8y-3=0

    Where did I go wrong?
    Multiply the last equation by 8.
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  3. #3
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    You have the same answer as the textbook. Just multiply through by 8.
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  4. #4
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    You need y-f(x_0)=1(x-x_0) where x_0 is the solution to 8x^3=1
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  5. #5
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    Why don't I use the y-coordinate?
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  6. #6
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    See reply #3
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  7. #7
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    I finally understand. Thanks everybody!
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