Horizontal Tangent Line Implicit Differentiation
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Notes
Questions
Find the equations of the horizontal tangent lines.
\(\textbf{1)}\) \( f(x)=10^two+4x+4 \)
The answer is \( y=0 \)
\(\textbf{ii)}\) \( f(ten)=\sin 10 \)
The respond is \( y=1 \) and \( y=-ane \)
\(\textbf{3)}\) \( f(x)=4 \)
The respond is \( y=4 \)
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\(\bullet\text{ Derivatives- Quotient Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}\left[\displaystyle\frac{f(x)}{g(10)}\right]=\displaystyle\frac{g(x) \cdot f'(x)-f(x) \cdot g'(x)}{[g(10)]^2}\)
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\(\bullet\text{ Derivatives- ln(10)}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[ln(x)]= \displaystyle \frac{ane}{10}\)
\(\bullet\text{ Implicit Differentiation}\)
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\(\bullet\text{ Horizontal Tangent Line}\)
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