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Math Help - find the gradient at the following points at the given (part2)

  1. #1
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    find the gradient at the following points at the given (part2)

    hi,
    i don't understand how i would find the gradient at the following points at the given points:
    y=3/x+2x+1 x=7

    i know i would do:
    y=3x^-1+2x+1
    dy/dx=-3x^-2+2

    im stuck after this because is i substitute it it looks like this:
    dy/dx=-21^-2+2

    what would i do from here??

    thanks!
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: find the gradient at the following points at the given (part2)

    Is y=\frac{3}{x+2x+1} or y=\frac{3}{x}+2x+1 ?
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  3. #3
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    Re: find the gradient at the following points at the given (part2)

    the second one, soory for the confusion!
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  4. #4
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    Re: find the gradient at the following points at the given (part2)

    Quote Originally Posted by andyboy179 View Post
    hi,
    i don't understand how i would find the gradient at the following points at the given points:
    y=3/x+2x+1 x=7

    i know i would do:
    y=3x^-1+2x+1
    dy/dx=-3x^-2+2
    Correct

    im stuck after this because is i substitute it it looks like this:
    dy/dx=-21^-2+2

    what would i do from here??

    thanks!
    That's an incorrect substitution: -3x^{-2} +2 = -\dfrac{3}{x^2} + 2. You appear to have included -3 in the exponent which is not the case.
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  5. #5
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    Re: find the gradient at the following points at the given (part2)

    i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?
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  6. #6
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    Re: find the gradient at the following points at the given (part2)

    Quote Originally Posted by andyboy179 View Post
    i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?
    -3 is not squared, only the 7 is squared. What you want to do is -3 \times \left(7^{-2}\right)
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  7. #7
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    Re: find the gradient at the following points at the given (part2)

    oh, so it would be 7^2= 49 then dy/dx=-3/49+2?
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  8. #8
    MHF Contributor Siron's Avatar
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    Re: find the gradient at the following points at the given (part2)

    Correct!
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  9. #9
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    Re: find the gradient at the following points at the given (part2)

    so is dy/dx=-3/49+2 the gradient?
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  10. #10
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    Re: find the gradient at the following points at the given (part2)

    Quote Originally Posted by andyboy179 View Post
    so is dy/dx=-3/49+2 the gradient?
    Indeed! The gradient of the tangent line in the point x=7
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  11. #11
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    Re: find the gradient at the following points at the given (part2)

    Quote Originally Posted by andyboy179 View Post
    so is dy/dx=-3/49+2 the gradient?
    Yes although since they are both numbers you should combine like terms to simplify your answer. I suggest writing 2 = \dfrac{98}{49} and get \dfrac{-3}{49} + \dfrac{98}{49} = \dfrac{95}{49}
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