The function is and tangent passes the point is
.
Let be the point at which tangent line intersects the curve.
Substitute in the function.
.
Point of tangency is .
Apply derivative on each side with respect to .
Quotient rule of derivatives : .
.
Slope of the tangent line is derivative of the function at .
Substitute in the derivative function.
.
Slope of the tangent line to the curve at the point is
.
Slope of a tangent line : .
Slope of a tangent line with points and
is
.
Slope of the tangent line to the curve is .
Substitute in the slope of the tangent line.
and
and
.
Substitute in the function.
Point of tangency is .
Substitute in the function.
Point of tangency is .
Find the tangent line.
\Point-slope form of line equation : , where slope
.
Find the tangent line equation passing through the points and
.
Tangent line equation is .
Find the tangent line equation passing through the points and
.
Tangent line equation is .
Graph :
\Graph the function and the two tangent lines.
\Tangent line equations is and
.