Question
Given
, write the equation of the line tangent to
when
Ask by Salazar Lane. in the United States
Jan 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the tangent line to
at
is:
Solution

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To find the equation of the tangent line to
at
, we first need to calculate
and then find the derivative
.
-
Calculate
: Since, -
Find
:
Using the chain rule,Now, we need to evaluate: Knowing, Therefore, -
Now we have the point
and the slope . The equation of the tangent line in point-slope form is: Simplifying gives:Rearranging gives the tangent line’s equation:
Thus, the equation of the tangent line is: