Finding the Tangent Line at y = x * e^(2x) | (2, 2*e^(4)) - Homework Solution

[Justabeginner]

Homework Statement

Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4))

Homework Equations

The Attempt at a Solution

f'(x)= e^(2x) * (2x+ 1)
(e^4)(5) = 5e^4
y- 2*e^4 = 5*e^4 (x-2)
y= 5(e^4)*x - 8*(e^4)

Is this right? It seems too easy for me to have gotten it right :/ Thanks.

 

[Mark44]

Homework Statement

Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4))

Homework Equations

The Attempt at a Solution

f'(x)= e^(2x) * (2x+ 1)
(e^4)(5) = 5e^4

To clarify, the above should be
f'(2) = (e^4)(5) = 5e^4
You're finding the slope of the tangent line when x = 2.

y- 2*e^4 = 5*e^4 (x-2)
y= 5(e^4)*x - 8*(e^4)

Is this right? It seems too easy for me to have gotten it right :/ Thanks.

Looks OK.
If you understand the steps involved (find the slope of the tangent, use the point-slope form of the line), it's not very hard.

 

[Justabeginner]

Yes sir, that is what I got! Thank you very much.

 

[Mark44]

You're welcome!