# A few quick questions!

• Jan 20th 2009, 02:42 PM
Sculthorp
A few quick questions!
Hey! A few questions here:

1) Find the equation of the tangent line to the parabola y=6-5x+3x^2 at the point where x=1. I got y=x+3... but the book says y=x+2.

2) Fine the equation of both tangent lines to the curve y=x^3-x that are parallel to the line 22x-2y+1=0. I understand y=11x+16.. but not the second answer.. y=11x-16.

3) What's the derivative of 5^x-1?

ANY HELP IS VERY, VERY, VERY MUCH APPRECIATED! Thanks. :)
• Jan 20th 2009, 03:02 PM
skeeter
Quote:

Originally Posted by Sculthorp
Hey! A few questions here:

1) Find the equation of the tangent line to the parabola y=6-5x+3x^2 at the point where x=1. I got y=x+3... but the book says y=x+2.

y(1) = 4
y' = -5 + 6x
y'(1) = 1

y - 4 = 1(x - 1)
y = x + 3

correct

2) Fine the equation of both tangent lines to the curve y=x^3-x that are parallel to the line 22x-2y+1=0. I understand y=11x+16.. but not the second answer.. y=11x-16.

22x - 2y + 1 = 0 has slope, m = 11

y' = 3x^2 - 1 = 11

x = 2 ... y = 6

y - 6 = 11(x - 2)

y = 11x - 16

x = -2 ... y = -6

y + 6 = 11(x + 2)

y = 11x + 16

3) What's the derivative of 5^x-1?

$5^x - 1$ or $5^{x-1}$ ?

ok?
• Jan 20th 2009, 03:07 PM
Sculthorp
Thanks so much! I meant $5^{x-1}$ though!
• Jan 20th 2009, 03:21 PM
skeeter
if $u$ is a function of $x$ and $a$ is a positive constant ...

$\frac{d}{dx} [a^u] = a^u \cdot \frac{du}{dx} \cdot \ln{a}$