How can I go about finding a tangent line for the following:

(x^3)*(R^5)=1 at the point (x,R)=(1,1)

I took the derivative of the equation but I didn't know where to go after that.

Printable View

- Oct 21st 2012, 01:13 PMsmgrojeanFinding a Tangent Line
How can I go about finding a tangent line for the following:

(x^3)*(R^5)=1 at the point (x,R)=(1,1)

I took the derivative of the equation but I didn't know where to go after that. - Oct 21st 2012, 01:40 PMskeeterRe: Finding a Tangent Line
is the slope of the curve at any point on the curve ...

evaluate the derivative at , to find the slope of the tangent line at that specific point, then use the point-slope form of a linear equation ...

- Oct 23rd 2012, 04:28 PMsmgrojeanRe: Finding a Tangent Line
So if I take the derivative I get:

3*R^5*X^2

Then if I evaluate that at x=1, R=1 I get:

3*1^5*1^2 = 3

So the point slope of the linear equation should be the following:

R - 1 = 3 ( X - 1) - Oct 23rd 2012, 06:10 PMProve ItRe: Finding a Tangent Line
That is not the derivative. Since R is a function of x, you will need to use implicit differentiation.

- Oct 23rd 2012, 06:25 PMskeeterRe: Finding a Tangent Line

solve for in terms of ...

... now find - Oct 26th 2012, 01:37 PMsmgrojeanRe: Finding a Tangent Line
so the derivative would actually be:

dr/dx = -3/(5*x^(8/5)) - Oct 26th 2012, 02:53 PMskeeterRe: Finding a Tangent Line
ok ... find the equation of the tangent line.

- Oct 28th 2012, 12:26 PMsmgrojeanRe: Finding a Tangent Line
so the equation should be:

R - 1 = -3/5(x-1)