Linear Approximation

**Velvet Love** · November 12th 2009, 02:01 PM

Find the linear approximation to f(x) = sqrt(1-4x) at x=-2

I keep getting (-2/3)*x +(13/3) as the answer, but it is wrong?

**skeeter** · November 12th 2009, 02:07 PM

Originally Posted by Velvet Love

Find the linear approximation to f(x) = sqrt(1-4x) at x=-2

I keep getting (-2/3)*x +(13/3) as the answer, but it is wrong?

check your arithmetic ... I get

$y = -\frac{2}{3}x + \frac{5}{3}$

**artvandalay11** · November 12th 2009, 02:12 PM

yes you took the derivative correctly, but it looks like something went wrong when you brought 3 over from the left hand side, or maybe when you multiplied through by $-\frac{2}{3}$

**Velvet Love** · November 12th 2009, 02:12 PM

Can you show me the steps? I do everything by the book, and i still get that answer.

**artvandalay11** · November 12th 2009, 02:14 PM

Originally Posted by Velvet Love

Can you show me the steps? I do everything by the book, and i still get that answer.

The equation of the tangent line is

$y-b=m(x-a)$

m is your derivative evaluated at a, which you did correctly, so what went wrong was solving for y after that, it's an error in your arithmetic

$y-3=-\frac{2}{3}(x-(-2))$

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