Check the solution to "How do you find the equation of the..."

Henry Winters

Answered question

2022-04-16

How do you find the equation of the line tangent to the graph of

y = e^{- x^{2}}

at the point

(2, \frac{1}{e^{4}})

glajusv8iv

Beginner2022-04-17Added 10 answers

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}} \Rightarrow y^{'} = - 2 x e^{- x^{2}}

sub x=2 into derivative function

y^{'} (2) = - 4 e^{- 4}

so we have found that the tangent line is

y = (- 4 e^{- 4}) x + c

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

\frac{1}{e^{4}} = (- 4 e^{- 4}) (2) + c

c = 9 e^{- 4}

so the tangent line is equal to

y = (- 4 e^{- 4}) x + 9 e^{- 4}

which can be simplified to:

y = - (4 x - 9) e^{- 4}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?