How do you find the equation of the line tangent to the graph of #y = e^(-x^2)# at the point (2, 1/e^4)?

1 Answer
Andre R.
Oct 22, 2016
  1. find derivative of function
  2. sub in x value of point to find gradient of tangent
  3. put gradient into y=(gradient)x+c
  4. Sub in point and solve for c
  5. you have found the equation of the tangent.

Explanation:

To find the Equation of a tangent to any curve you must first find the derivative of the function.
For example for #y= e^(-x^2)# => #y'= -2x e^(-x^2)#

sub x=2 into derivative function
#y'(2) = -4e^-4#
so we have found that the tangent line is
#y=(-4e^-4)x + c#

so now we have to sub in the point and solve for c:

#1/e^4=(-4e^-4)(2) + c#
c= #9e^-4#
so the tangent line is equal to
#y=(-4e^-4)x + 9e^-4#
which can be simplified to:
#y=-(4x-9)e^-4#

hope that helped.

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