# How to find the derivative of a graph

**Secant Lines and the Slope of a Curve**

The following applet can be used to approximate the slope of the curve *y=f(x)* at *x=a*. Simply enter the function *f(x)* and the values *a* and *b*. The applet automatically draws the secant line through the points *(a,f(a))* and *(b,f(b))*. As *b* approaches *a*. the slope of the secant line approaches the slope of the line tangent to *f(x)* at *x=a*.

By selecting "*h=* " instead of "*b=* ", the applet automatically draws the secant line through the points *(a,f(a))* and *(a+h,f(a+h))*. As *h* approaches *0*. the slope of the secant line approaches the slope of the line tangent to *f(x)* at *x=a*. In other words,

the applet can be used to investigate the following two equivalent definitions for the derivative of *f(x)* at *x=a*.

The values *a*. *b* and/or *h* can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the *x* -axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.

Source: www.personal.psu.edu

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