Posted by **Allison** on Saturday, March 12, 2011 at 8:14pm.

if x=e^t and y=(t-3)^2 , find an equation y=mx+b of the tangent to the curve at (1,9).

- Calculus -
**bobpursley**, Saturday, March 12, 2011 at 8:28pm
dy/dx=2(t-3)dt/dx

but

dx/dt=e^t, so

dy/dx=2(t-3)e^-t

so m= that. Now when x=1, (x=e^t), t must be zero, so

m=2(-3)=-6

y=-6x+b

now, at point 1,9

9=-6+b,or b=15, so equation for line must be

y=-6x+15

check that.

- Calculus -
**Allison**, Saturday, March 12, 2011 at 8:46pm
I just figured it out! thank you!

## Answer This Question

## Related Questions

- Calculus - Please help this is due tomorrow and I don't know how to Ive missed a...
- calculus - Find an equation of the tangent(s) to the curve at a given point. ...
- Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...
- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- Calculus AB - Sorry but I've got a lot of problems that I don't understand. 1) ...
- Calculus 1 - The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. ...
- Calculus 1 - The curve y =|x|/(sqrt(5−x^2)) is called a bullet-nose curve...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- calculus - Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx...
- AP AB Calculus - Linear approximation: Consider the curve defined by -8x^2 + 5xy...

More Related Questions