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.

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