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How could I find the equation of the tangent line to the curve with equation y=(x^2-3)^5 at the point (2,1)? 

 Jul 26, 2021
 #1
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The first derivative will give you the slope at  x = 2     ( from the point 2,1)

 

10x (x^2-3)^4     when x = 2

10(2)(4-2)^4 = 20 = the  slope at x = 2

 

y = mx + b

y = 20x + b      for the point 2,1

1 = 20(2) + b      b = -39

 

y = 20x - 39

 

 

Here is a graph to confirm:

https://www.desmos.com/calculator/eqlln3qpv9

 Jul 26, 2021

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