Homework Help: Calculus

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

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3.
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 10:58pm
I 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 - Tangent Line - Hi, im having problems with the following problem. The...
Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
Calculus - Use the given equation to answer the following questions. (Enter your...
calculus - Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) ...
Calculus - Find an equation of the tangent line to the curve at the given point...
Calculus - (a) Find dy/dx given that x^2+y^2-4x+7y=15. (b) Under what conditions...
calculus - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...
Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...
Calculus - Consider line segments which are tangent to a point on the right ...
calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...

For Further Reading

First Name:
School Subject:
Answer: