How to find the slope of a tangent line

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Geometry › How to find the slope of a tangent line

Questions 1 - 3

1

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

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 .

2

Suppose the equation of a line is . What is the slope of the tangent line at ?

$\frac{3}{5}$

$-\frac{9}{5}$

$\frac{9}{5}$

$\frac{5}{3}$

Explanation

Rewrite in slope-intercept form, .

$y=\frac{3}{5}x-\frac{3}{5}$

The slope of the tangent line is $\frac{3}{5}$ .

3

Suppose a function . What is the slope of the tangent line at ?

$\textup{There is no slope.}$

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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