Precalculus aid » introductory Calculus » Tangents to a Curve » find the Equation of a heat Tangent come a Curve in ~ a Given point

Find the equation of the heat tangent to the graph of 

*

at the point 

*
 in slope-intercept form.

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Explanation:

We start by recalling that one way of specifying the derivative that a function is the slope of the tangent line of the role at a given point. Therefore, detect the derivative of ours equation will permit us to find the slope of the tangent line. Since the 2 things required to discover the equation that a line space the slope and a point, we would be halfway done.

We calculate the derivative making use of the strength rule.

*

However, we don"t desire the steep of the tangent line at just any allude but quite specifically at the point 

*
. To obtain this, we simply substitute our x-value 1 into the derivative.

*

Therefore, the steep of ours tangent line is 

*
.

We now require a suggest on our tangent line. Our options are rather limited, as the only point on the tangent line that we understand is the suggest where the intersects our original graph, namely the point 

*
.

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Therefore, we can plug this coordinates along with our slope right into the general point-slope form to find the equation.