The discussion revolves around finding the equation of the tangent line to the curve defined by y = x * e^(2x) at the specific point (2, 2*e^(4)). Participants are exploring the differentiation of the function and the application of the point-slope form of a line.
Some participants express uncertainty about the correctness of their solutions, while others affirm that the steps taken appear valid. There is a general acknowledgment of the process involved in finding the tangent line, but no explicit consensus on the final answer.
Participants are working under the constraints of a homework assignment, which may influence their approach and the level of detail they provide in their reasoning.
To clarify, the above should beJustabeginner said: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
Justabeginner said: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.