The function is and point
.
Slope of the tangent line is the derivative of the function at .
Consider .
Apply derivative on each side with respect to .
.
Power rule of derivatives : .
Constant rule of derivatives :.
.
Substitute in
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Slope of the tangent line is .
Find the tangent line equation.
\Point slope form of line equation : .
Substitute and
in the point-slope form.
The tangent line equation is .
Graph:
\Graph the function and tangent line
.
The differential equation is .
The tangent line equation is .