Find the equation of the tangent line to at x = 1. |
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Step 1: Find the tangent point, . You need to evaluate your given equation, , at the given x-value to find the y-value , .
In this example . You need to find in order to get our . |
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Step 2: Find the slope , m , of the tangent line. The slope of the tangent line is found by evaluating your derivative at the given x-value , .
To do this you will need to start by finding your actual . Keep in mind that finding the derivative is now just a small part of a larger process.
Finding this derivative will require an algebraic rewrite (power over root) . After that you would follow the chain-rule process to get the derivative result, .
Now to find the actual slope , m , of the tangent line, we will need to plug our x-value into that derivative equation, . |
Calculus complete, begin algebra.
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Step 3: Find the equation of the tangent line.
You grab your point, , from
Step 1
, your , from
Step 2
, and you plug them into point-slope form of a line,
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Final Result: The equation of the tangent line to the graph of , at x = 1 , is .
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