Friday

October 24, 2014

October 24, 2014

Posted by **Lauren** on Tuesday, March 31, 2009 at 10:34pm.

We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of the tangent line at x=3 is 5/2

A. Let c(x)= 1/r(x). Find c'(3).

I used the quotient rule (for clarity, I am substituting "a" for r(x))

c'(x)= (a[0] - 1a')/a^2

Which reduces to

-a'/a^2

Replacing r(x) at x=3 for a, we get:

-r'(3)/(r(3))^2

Since the derivative of r(x) at 3 is equal to the slope of the tangent line at x=3, we get

-(5/2)/(8)^2 or -5/128

Does that look correct?

b. Let i(x) = the inverse of r(x). Find i'(8).

I had some trouble with this one. I know that the point (3,8) is on r(x) (from the given information in part a). This would mean that if i(x) is the inverse of r(x), then (8,3) would be on i(x). I also know that r'(3)=5/2. Because derivatives of inverses are reciprocals at corresponding points, would this mean that i'(8)=2/5?

- Calculus -
**Reiny**, Tuesday, March 31, 2009 at 10:58pmI agree with your thinking for both questions.

I especially like that you realize the relationship of slopes between corresponding points on a relation and its inverse.

**Answer this Question**

**Related Questions**

Calculus - Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x...

Calculus - Tangent Line - Hi, im having problems with the following problem. The...

calculus - Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) ...

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

Calculus - (a) Find dy/dx given that x^2+y^2-4x+7y=15. (b) Under what conditions...

AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...

Calculus - Use the given equation to answer the following questions. (Enter your...

Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...

Calculus - Find an equation of the tangent line to the curve at the given point...

calculus - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...