All Intermediate Geometry Resources
Example Question #221 : Lines
What is the slope of the tangent line to the graph of when ?
To find the slope of the tangent line, first we must take the derivative of , giving us . Next we simply plug in our given x-value, which in this case is . This leaves us with a slope of .
Example Question #222 : Lines
Suppose the equation of a line is . What is the slope of the tangent line at ?
Rewrite in slope-intercept form, .
The slope of the tangent line is .
Example Question #223 : Lines
Suppose a function . What is the slope of the tangent line at ?
Write the formula for slope-intercept form.
The slope of is always zero at every point on the domain. Therefore, the slope at must also be zero.