Precalculus Aid » Introductory Calculus » Tangents To a Curve » Find the Equation of a Line Tangent to a Curve At a Given Point

Find the equation of the line tangent to the graph of 

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at the point 

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 in slope-intercept form.

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Explanation:

We start by recalling that one method of defining the derivative of a function is the slope of the tangent line of the attribute at a offered point. Therefore, finding the derivative of our equation will certainly permit us to discover the slope of the tangent line. Since the 2 things necessary to uncover the equation of a line are the slope and also a allude, we would be halfmeans done.

We calculate the derivative using the power rule.

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However, we do not desire the slope of the tangent line at simply any kind of point yet fairly specifically at the point 

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. To achieve this, we simply substitute our x-value 1 right into the derivative.

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As such, the slope of our tangent line is 

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.

We now require a suggest on our tangent line. Our options are fairly limited, as the just point on the tangent line that we recognize is the allude wright here it intersects our original graph, namely the point 

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.

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Thus, we have the right to plug these works with along with our slope into the general point-slope create to discover the equation.