Intermediate Geometry : How to find the slope of a tangent line

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #221 : Lines

What is the slope of the tangent line to the graph of  when ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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.

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