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Math Help - Curve + tangent

  1. #16
    A Plied Mathematician
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    By "where do they solve it", I mean "where are the solutions?" You've found them. There's really only one step left. What do you suppose that is?
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  2. #17
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    Quote Originally Posted by Ackbeet View Post
    By "where do they solve it", I mean "where are the solutions?" You've found them. There's really only one step left. What do you suppose that is?
    provide a general solution?
    show that these values of x satisfy the original equation?
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  3. #18
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    You've found the locations where the line y = x equals the original function. But how do you know that, at those points, y = x touches the original function?
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  4. #19
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    Quote Originally Posted by Ackbeet View Post
    You've found the locations where the line y = x equals the original function. But how do you know that, at those points, y = x touches the original function?
    at the points where y=x touches the original function the gradients are equal
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  5. #20
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    True... but how do you know that?
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  6. #21
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    Quote Originally Posted by Ackbeet View Post
    True... but how do you know that?
    ermm.. because the line y=x is a tangent to the curve? Thus at the point where it is a tangent its gradient is equal to that of the curve?

    I'm sorry Im doing really bad with this one!
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  7. #22
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    Hint: evaluate the _____________ at the points of touching, and show that they're all equal to __ .
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  8. #23
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    Quote Originally Posted by Ackbeet View Post
    Hint: evaluate the _____________ at the points of touching, and show that they're all equal to __ .
    evaluate the gradient at the points of touching, and show that they're all equal to 1?

    ie. when x = 5pi/2, dy/dx = 1
    when x = 9pi/2, dy/dx = 1
    ...
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  9. #24
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    You got it. I would say that once you've shown all that, you're done with this problem.
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  10. #25
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    Thank you soooo much! You've been such a great help
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  11. #26
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    You're very welcome. Have a good one!
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