Problem

Find equations of the tangent line and normal lin…

01:44

Problem 33 Medium Difficulty

Find equations of the tangent line and normal line to the given curve at the specified point.

$ y = 2xe^x, (0,0) $

Answer

tangent line is $y-0=2$
normal line is $-\frac{1}{2}$

Discussion

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Video Transcript

it's Clarissa when you right here. So we have acts is equal to two x e to the X To find the derivative, we got D over DX. To exceeds the X, we used the product Rule two x d to the axe eat the X plus eat the X d over DX for two X this becomes equal to eat. The axe comes to X plus two and the slope of detention at 00 becomes too. So the equation of attention is why equals two X? We have to note that while we multiply perpendicular lines, there slope is negative one. So the normal normal line has a slope of negative 1/2. So the equation of the normal line is gonna be Y minus zero over X minus zero, which is equal to negative one tough ex. So this becomes a Y is equal to negative 1/2 X for the normal line.

Clarissa N.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Problem