How To Find Horizontal Tangent
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Notes
Questions
Detect the equations of the horizontal tangent lines.
\(\textbf{1)}\) \( f(x)=10^two+4x+4 \)
The respond is \( y=0 \)
\(\textbf{ii)}\) \( f(x)=\sin ten \)
The answer is \( y=one \) and \( y=-1 \)
\(\textbf{3)}\) \( f(x)=four \)
The respond is \( y=4 \)
See Related Pages\(\)
\(\bullet\text{ Definition of Derivative}\)
\(\,\,\,\,\,\,\,\, \displaystyle \lim_{\Delta x\to 0} \frac{f(x+ \Delta ten)-f(x)}{\Delta x} \)
\(\bullet\text{ Equation of the Tangent Line}\)
\(\,\,\,\,\,\,\,\,f(ten)=x^iii+3x^two−10 \text{ at the betoken } (two,18)\)
\(\bullet\text{ Derivatives- Constant Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(c)=0\)
\(\bullet\text{ Derivatives- Ability Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(10^due north)=nx^{n-i}\)
\(\bullet\text{ Derivatives- Constant Multiple Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}(cf(ten))=cf'(x)\)
\(\bullet\text{ Derivatives- Sum and Divergence Rules}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(x) \pm g(x)]=f'(x) \pm g'(x)\)
\(\bullet\text{ Derivatives- Sin and Cos}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}sin(ten)=cos(x)\)
\(\bullet\text{ Derivatives- Product Dominion}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(ten) \cdot g(ten)]=f(x) \cdot 1000'(x)+f'(x) \cdot g(x)\)
\(\bullet\text{ Derivatives- Quotient Rule}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}\left[\displaystyle\frac{f(x)}{g(10)}\correct]=\displaystyle\frac{thou(x) \cdot f'(x)-f(10) \cdot g'(ten)}{[yard(x)]^2}\)
\(\bullet\text{ Derivatives- Concatenation Dominion}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[f(thou(ten))]= f'(thou(x)) \cdot chiliad'(x)\)
\(\bullet\text{ Derivatives- ln(x)}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[ln(10)]= \displaystyle \frac{1}{x}\)
\(\bullet\text{ Implicit Differentiation}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Horizontal Tangent Line}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Mean Value Theorem}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Related Rates}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Increasing and Decreasing Intervals}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Intervals of concave up and downward}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Inflection Points}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Graph of f(ten), f'(x) and f"(10)}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Newton's Method}\)
\(\,\,\,\,\,\,\,\,x_{n+1}=x_n – \displaystyle \frac{f(x_n)}{f'(x_n)}\)
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How To Find Horizontal Tangent,
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