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Math Help - Very Simple Differentiation

  1. #1
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    Very Simple Differentiation

    The tangent to the curve y=ax˛+bx at the point where x=1 has a gradient 1 and passes through point (4,5). Find a and b. Question is frustrating me .

    Here's what I've got.

    dy/dx = 2ax+b

    (For x=1) 2a+b=1

    Using curve and other given point: 5=16a+4b

    Now when I put these into a sim eqation and solve it's wrong :/ I have no idea why either.
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  2. #2
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    Quote Originally Posted by alibond07 View Post
    The tangent to the curve y=ax˛+bx at the point where x=1 has a gradient 1 and passes through point (4,5). Find a and b. Question is frustrating me .

    Here's what I've got.

    dy/dx = 2ax+b

    (For x=1) 2a+b=1

    Using curve and other given point: 5=16a+4b

    Now when I put these into a sim eqation and solve it's wrong :/ I have no idea why either.
    Your working up to here is fine so not sure where you went wrong. Using your equations I arrived at the right answer so I'm guessing it's an arithmetic problem

    Rearrange the first equation b = 1-2a

    5=16a+4(1-2a) = 8a+4 \: \: \therefore \: \: a = \frac{1}{8}

    b = 1-\frac{2}{8} = \frac{3}{4}

    Verify using (4,5) and f(x)

    y = \frac{16}{8}+\frac{4 \times 3}{4} = 2+3 = 5
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Your working up to here is fine so not sure where you went wrong. Using your equations I arrived at the right answer so I'm guessing it's an arithmetic problem

    Rearrange the first equation b = 1-2a

    5=16a+4(1-2a) = 8a+4 \: \: \therefore \: \: a = \frac{1}{8}

    b = 1-\frac{2}{8} = \frac{3}{4}

    Verify using (4,5) and f(x)

    y = \frac{16}{8}+\frac{4 \times 3}{4} = 2+3 = 5
    Same as what I got : / , in the book they state it as, A= -1 B=-3. Maybe a mistake in the book? That dosen't seem to happen ever though : /
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  4. #4
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    Quote Originally Posted by alibond07 View Post
    Same as what I got : / , in the book they state it as, A= -1 B=-3. Maybe a mistake in the book? That dosen't seem to happen ever though : /
    Try subbing in those values:

    y = 16(-1)+(-3)(4) = -16-12 = -28

    Obviously -28 \neq 5 so the book is wrong
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