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Math Help - Chain rule for exponential functions

  1. #1
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    Chain rule for exponential functions

    I have a question I could use a little help with here...

    Find the equation of the tangent to the function f(x) = 3^(x^2+1) - x^2 at (1 , 8)


    I have used the difference rulwe and the chain rule for exp. functions to come up with the derivative:

    2x(3^(x^2+1)) (ln3) - 2x

    So using 1 for the value of x I come up with m = 17.77

    I have the solution to the question which shows one of the last few steps of the solution as:

    y = 17.77(x-1) + 8

    If the formula for the equation is y = mx + b.... Why does the solution have (x - 1) as the x value. And how did they come up with 8 as the y - intercept? Thanks!
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  2. #2
    MHF Contributor ebaines's Avatar
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    If you know that the equation for a line has slope m, and that it passes through the point (x1, y1), then it's equatoin is:

    <br />
\frac {y - y_1} {x - x_1} = m<br />

    or rearranging:
    <br />
y - y_1 = m(x-x_1)<br />

    So here you have:

    y-8 = 17.77(x-1)

    Which you can rearrange into y = mx+b form:

    y = 17.77(x-1) + 8.
    y = 17.77x -9.77

    The y-intercept of the line is therefore: -9.77
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  3. #3
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    Quote Originally Posted by ebaines View Post
    If you know that the equation for a line has slope m, and that it passes through the point (x1, y1), then it's equatoin is:

    <br />
\frac {y - y_1} {x - x_1} = m<br />

    or rearranging:
    <br />
y - y_1 = m(x-x_1)<br />

    So here you have:

    y-8 = 17.77(x-1)

    Which you can rearrange into y = mx+b form:

    y = 17.77(x-1) + 8.
    y = 17.77x -9.77

    The y-intercept of the line is therefore: -9.77
    Got it. Thanks!
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