Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By Plato

Thread: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate form

  1. #1
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    80

    y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate form

    y(x) = (5-x)^4 at x = 4
    how do I solve this equation with the instantaneous rate of change formula ? any help would be greatly appreciated .I know I use f'(x)=lim{f((x+h)-f(x))/h) but the polynomial is giving me trouble ....please help ..the answer is -4 from a quiz I did but I got it wrong .
    Bee
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,149
    Thanks
    2603
    Awards
    1

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    Quote Originally Posted by bee77 View Post
    y(x) = (5-x)^4 at x = 4
    how do I solve this equation with the instantaneous rate of change formula ? any help would be greatly appreciated .I know I use f'(x)=lim{f((x+h)-f(x))/h)
    Do you understand that $y(x) = (5-x)^4=(x-5)^4~?$ If you do not there is no point in your trying this question.
    To answer you must know that the instantaneous rate of change formula is simply: $y'(x)=4(x-5)^3$.
    So $y'(4)=-4$.
    Thanks from bee77
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    80

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    Thank you . So everytime I see something like this I just simply derive with the power rule and substitute?If a limit was added would I need to refer to the f'(x)=lim{f((x+h)-f(x))/h) formula?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    80

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    sorry the limit ->0 should have been added then
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,522
    Thanks
    958

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    Not quite...

    $\displaystyle f'(x) = \lim_{h \to 0} \dfrac{(f(x+h)-f(x))}{h}$

    $\displaystyle f'(x) \neq \lim_{h \to 0} \dfrac{f((x+h)-f(x))}{h}$

    Placement of parentheses is important.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,948
    Thanks
    3572

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    f'(x) = \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}

    f(x) = (5-x)^4$, $f(x+h) = [5-(x+h)]^4 = (5-x-h)^4

    let t = 5-x

    \lim_{h \to 0} \dfrac{(t-h)^4 - t^4}{h}

    \lim_{h \to 0} \dfrac{[(t-h)^2 - t^2][(t-h)^2 + t^2]}{h}

    \lim_{h \to 0} \dfrac{(t^2 - 2ht + h^2 - t^2)(t^2 - 2ht + h^2 + t^2)}{h}

     \lim_{h \to 0} \dfrac{h(h-2t)(2t^2-2ht+h^2)}{h}

    \lim_{h \to 0} \dfrac{\cancel{h}(h-2t)(2t^2-2ht+h^2)}{\cancel{h}} = -4t^3 = -4(5-x)^3

    f'(4) = -4(5-4)^3 = -4
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,105
    Thanks
    2800

    Re: y(x) = (5-x)^4 at x = 4 can anyone help me solve this with the intantaneous/rate

    Quote Originally Posted by bee77 View Post
    y(x) = (5-x)^4 at x = 4
    how do I solve this equation with the instantaneous rate of change formula ? any help would be greatly appreciated .I know I use f'(x)=lim{f((x+h)-f(x))/h) but the polynomial is giving me trouble ....please help ..the answer is -4 from a quiz I did but I got it wrong .
    Bee
    The way you have written this is very confusing! You say "solve this equation" but the given equation has two variables so that "solve the equation" makes no sense. And, it appears that you really want to "find the derivative of this function at x= 4. In any case, you should have shown us what you did and why you got "-4" so we could point out and correct any error.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] find the rate, solve for r
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Dec 8th 2011, 10:16 PM
  2. Crossover rate - How to solve r?
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Oct 12th 2011, 02:38 PM
  3. solve for interest rate
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Oct 17th 2009, 07:09 AM
  4. solve for interest rate
    Posted in the Business Math Forum
    Replies: 4
    Last Post: Aug 29th 2008, 07:14 AM
  5. How to solve interest rate to the ^5
    Posted in the Business Math Forum
    Replies: 2
    Last Post: Oct 27th 2007, 02:00 PM

/mathhelpforum @mathhelpforum