# Tangent line and velocity problems

• October 5th 2008, 04:25 PM
john11235
Tangent line and velocity problems
I'm having some trouble with some of these. It's kinda one of those times where you're doing great in class and then you leave and can't remember anything (Headbang)

1. If a rock is thrown in the air on a small planet with velocity 25 m/s, its height in meters is Y = 25t - 4.9t^2. What is the rock's velocity at t = 3?

2. The slope of the tangent line to the curve Y = 4(sqrt[x]) is _______. The equation for the line is Y = mx + b, where M is ______ and B is ______.
• October 5th 2008, 04:51 PM
skeeter
1. If a rock is thrown in the air on a small planet with velocity 25 m/s, its height in meters is Y = 25t - 4.9t^2. What is the rock's velocity at t = 3?

$v = \frac{dy}{dt}$

2. The slope of the tangent line to the curve Y = 4(sqrt[x]) is _______. The equation for the line is Y = mx + b, where M is ______ and B is ______.

slope = $\frac{dy}{dx}$, the derivative of $y = 4\sqrt{x}$

second sentence blanks are from algebra 1 ... don't make it out to be harder than it is. what does m represent? b ??
• October 5th 2008, 08:13 PM
john11235
Ok thanks. Now what would I do with:

Find f'(t) for f(t) = 12/(t^6)

and

Find f'(t) for f(t) = (3x)^5
• October 5th 2008, 09:03 PM
earboth
Quote:

Originally Posted by john11235
Ok thanks. Now what would I do with:

Find f'(t) for f(t) = 12/(t^6)

and

Find f'(t) for f(t) = (3x)^5

1. If you have a new question, please start a new thread.

2. Re-write

$f(t)=\dfrac{12}{t^6} = 12 \cdot t^{-6}$

Calculate $f'(t)=\dfrac{df}{dt}$ as usual but keep in mind that $-6 - 1 = -7$ :)

The second question is a trick question:

f(t) states that the variable is t. Therefore $(3x)^5$ is a constant here. And therefore $f'(t)=0$