Find the equation of the tangent line to the curve at
.
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Find the equation of the tangent line to the curve at
.
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First, we find the slope of the tangent line by finding the derivative of
at
.
Given:
.
Then,
and
.
Thus, the slope of the tangent line is 1.
Next, we find the y-coordinate of the function
at
.
At
.
Thus, the point of tangency is (-1, 2).
Finally, the equation of a line with a slope of
and passing through the point
is given as follows:
Therefore, the required equation is
.
We know that the equation of a tangent line of the curve on a function
at the point
with abscissa
is
, in our case
, so the equation is 
So let’s calculate
and
.
We have
Thus
Then
And
Therefore
Finaly