Math 22 The Derivative and the Slope of a Graph

Slope of a Graph

We can estimate the slope at the given point to be

Slope = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\Delta y}{\Delta x}=\frac {\text{change in y}}{\text{change in x}}}

Difference Quotient

 The slope $m$ of the graph of $f$ at the point $(x,f(x))$ can be 
 written as :
 
 $m=\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}$
 
 The right side of this equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac {f(x+h)-f(x)}{h}}
 is called Difference Quotient