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Likurg_2 [28]
3 years ago
13

Find the equation of the tangent line. y=(x^2+x-2)^2 at (-1,4)​

Mathematics
1 answer:
Keith_Richards [23]3 years ago
6 0

Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:

d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]

d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)

Evaluate the derivative at <em>x</em> = -1 :

d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4

This is the slope of the tangent line to the function at (-1, 4).

Use the point-slope formula to get the equation for the tangent line:

<em>y</em> - 4 = 4 (<em>x</em> - (-1))   →   <em>y</em> = 4<em>x</em> + 8

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