Pregunta
Find the equation of the line tangent to the graph of
at
. Use the point-slope form.
Include a multiplication sign between symbols. For example,
.
Include a multiplication sign between symbols. For example,
Ask by Osborne Mcdonald. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The equation of the tangent line is
.
Solución
-
Start with the function:
-
Compute the derivative to find the slope of the tangent line:
-
Evaluate the derivative at
to get the slope: -
Find the point on the curve at
: So the point is. -
Use the point-slope form of the equation of a line:where
and . -
Substitute the values into the point-slope form:
Thus, the equation of the tangent line is:
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Bonus Knowledge
To find the equation of the tangent line, we first need the derivative of
. The derivative,
, is calculated as follows:
Next, we evaluate the derivative at
:
This means the slope of the tangent line at
is
. Now, we calculate
:
Now we have a point on the tangent line,
, and the slope
. The point-slope form of the line is given by:
where
is the slope and
is the point. Substituting in our values:
This is the equation of the tangent line in point-slope form!

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