(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the tangent line and the normal line to the curve y=(1+2x)^2 at the point (1,9).

2. Relevant equations

f'(x)= [f(x+h) - f(x)] / h ->plug in x=1

f'(x)= [f(x+h) - f(x)] / h ->plug in (x+h)

Power Rule

Power Rule (after factoring out the polynomial)

3. The attempt at a solution

I tried to solve it 4 different ways using the above 4 different approaches:

Plugging in x=1 for the derivative formula yields 12

Plugging in (x+h) for the derivative formula yields 4+8x

Using the power rule for (1+2x)^2 = 2(1+2x) = 2+4x (simplified version of 4+8x)

Using the power rule after factoring out the polynomial is 1+4x+4x^2 = 4+8x

Regarding the first attempt, I thought I could plug in the x-coordinate to get the tangent equation. Since when is that wrong?

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# Homework Help: 3 different derivatives?

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