Posted by **Sasha** on Thursday, October 7, 2010 at 12:55am.

find an equation of the tangent line to the curve y = x √x that is parallel to the line y = 1 + 3x.

- calculus -
**MathMate**, Thursday, October 7, 2010 at 11:16am
y

=f(x)

=x√x

=x^{3/2}

Use the power rule for derivatives to get

f'(x)=(3/2)√x

For L: y=3x+1, the slope is 3.

Solve for x0 in

f'(x0)=3

Find the ordinate

y0=f(x0)

The point of tangency is therefore at (x0,y0).

Now pass a line L1 through (x0,y0) having a slope of 3:

(y-y0)=3(x-x0)

Check that the line has a slope of 3 and pass through the point (x0,y0)

## Answer this Question

## Related Questions

- calculus - find an equation of the tangent line to the curve y = x √x that...
- Math - In this problem we consider drawing some straight lines which form a nice...
- Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
- Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...
- collge calculus - find an equation of the tangent line to the curve y= x(x)^(1/2...
- Calculus - Find an equation of the tangent line to the given curve at the given ...
- Calculus - 1. On what interval is the function f(x)=x^3-4x^2+5x concave upward? ...
- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- Math - Can someone help me with this problem? Find the equation of the tangent ...
- calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...

More Related Questions