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)

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