# calculus

posted by .

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

• calculus -

y
=f(x)
=x√x
=x3/2
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)

## Similar Questions

1. ### Calculus

Find an equation of the tangent line to the given curve at the given point y=(1/cosx)-2cosx at((pi/3),1) y'=0+2sinx slope = √3 y=mx+b 1=(√3)(pi/3)+b b=(3-√3pi)/3 3√3x-3y+3-√3pi=0 What did I do wrong?
2. ### calculus

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

find an equation of the tangent line to the curve y= x(x)^(1/2) that is parallel to the line y=1+3x
4. ### Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
5. ### Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x …
6. ### Calculus

1. On what interval is the function f(x)=x^3-4x^2+5x concave upward?
7. ### Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, …
8. ### calculus

Find the point on the curve y =2/3 〖√(18-x^2 )〗 (first quadrant) where a tangent line may be drawn so that the area of the triangle formed by the tangent line and the coordinate axes is a minimum.
9. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?