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 = ${\frac {\Delta y}{\Delta x}}={\frac {\text{change in y}}{\text{change in x}}}$

Difference Quotient

 The slope Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m}
 of the graph of $f$ at the point 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 (x,f(x))}
 can be 
 written as :
 
 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 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 \lim_{h\to 0}\frac {f(x+h)-f(x)}{h}}
 is called Difference Quotient