[SOLVED] Find equations of the tangent line...

**moonman** · March 12th 2009, 10:43 AM

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

Y = 2xe^(x) , (0,0)

**Air** · March 12th 2009, 11:01 AM

Originally Posted by moonman

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

Y = 2xe^(x) , (0,0)

A tangent line is a straight line that touches a function at only one point. The slope of the tangent line (the gradient) at a point on the function is equal to the derivative of the function at the same point.

$y=2xe^x$

$\frac{\mathrm{d}y}{\mathrm{d}x} = 2xe^x + 2e^x$ . At $(0,0)$ , The tangent gradient equals $m = 2(0)e^0 + 2e^0 = 2$

Equation of tangent: $y-0 = 2(x-0) \rightarrow y = 2x$

The equation of Normal line has the same coordinate of intersection $(0,0)$ and the same y-intercept but the gradient is different. The gradient of the normal line is $n = -\frac{1}{m} = -\frac{1}{2}$ where $m$ is the gradient of the tangent line and $n$ is the gradient of the normal line.

This Equation of normal line: $y-0 = -\frac12 (x-0) \rightarrow y = -\frac12 x$

Thread: [SOLVED] Find equations of the tangent line...

LinkBack

Thread Tools

Display

[SOLVED] Find equations of the tangent line...

Similar Math Help Forum Discussions

Find the parametric equations of the tangent line to a line (Answer included)

Find an Equation of the Tangent Line to the parabola at the given point and find....

Find the equations of the tangent plane and the normal line to the given surface

Tangent line equations

[SOLVED] Tangent Line/Secant Line To A Parabola

Search Tags