Posted by **Alia** on Monday, October 17, 2011 at 7:23am.

Given that y=x^(5/2)- x^(-1/2) .

a) Find the coordinates where the tangent line is parallel to the line y-4x-4=0.

b) Find the coordinates where the tangent line is perpendicular to the line 2y-3x-12=0.

- Calculus -
**Steve**, Monday, October 17, 2011 at 2:17pm
First find the slope of the tangent line = y'

y' = 5/2 * x^(3/2) + 1/2 * x^(-3/2)

The line in question has slope m=4

So, you want y'=4

5/2 * x^(3/2) + 1/2 * x^(-3/2) = 4

let u = x^(3/2) We can rewrite that as

5u/2 + 1/2u = 4

Multiply by 2u

5u^2 + 1 = 8u

5u^2 - 8u + 1 = 0

u = 1.46332 or 0.13667

so, x = u^(2/3) = 1.2889 or .26532

Evaluate y for those values of x to get the actual points.

for the perpendicular line, the slope m = -2/3. Do the same steps.

## Answer This Question

## Related Questions

- Calculus - Given the function y=(x^2-5/x+3), answer the following questions. a) ...
- Calculus - Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why ...
- Calculus - Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why ...
- calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...
- Geometry - Prove that the tangents to a circle at the endpoints of a diameter ...
- calculous - 3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the ...
- Calculus AB - Could someone please help me with these tangent line problems? 1) ...
- calculus - Determine the coordinates of the point on the graph of f(x)= (2x+1)^(...
- Calculus - Determine the coordinates of the point on the graph of f(x)=3x^2-7x+4...
- Calculus - I have a two part question that pertains to a curve (r(x)) and its ...

More Related Questions