1. If an arrow is shot straight upward on the moon with a velocity of 78 m/s, its height (in meters) after t seconds is given by .
What is the velocity of the arrow (in m/s) after 7 seconds? 66.38 m/s

After how many seconds will the arrow hit the moon? 94 seconds
With what velocity (in m/s) will the arrow hit the moon? How do you find this?? Is it 78 m/s?

2. If
find the values of and that make differentiable everywhere.
Find m=? and b=?

3. Given that

Calculate 6
Calculate -8
Calculate ( -7)
Calculate (-1/7)
Both answers for (f*g) and (f/g) are wrong...does anyone know why?

2. Originally Posted by Kayla_N
3. Given that

Calculate 6
Calculate -8
Calculate i cant figure this out??
Calculate This one too?
Calculate i cant figure this out??
f'(3)*g'(3) = (-1*7)=-7

Calculate This one too?
f'(3)/g'(3) = (-1/7)= $-\frac 1 7$

3. I got that answer too..but its not right. I dont understand what they looking for??

4. With what velocity (in m/s) will the arrow hit the moon? How do you find this?? Is it 78 m/s?
velocity is the derivative of position ...

$v(t) = 78 - 1.66t$

2. If
find the values of and that make differentiable everywhere.
Find m=? and b=?
function needs to be continuous ...
f(10) = 100 , so 100 = m(10) + b

to be differentiable ...
f'(10) = 20, so 20 = m ... b = -100

Both answers for (f*g) and (f/g) are wrong...does anyone know why?
product rule ...

$(f \cdot g)'(x) = f(x) \cdot g'(x) + g(x) \cdot f'(x)
$

quotient rule ...

$\left(\frac{f}{g}\right)'(x) = \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{[g(x)]^2}$

5. Originally Posted by skeeter

function needs to be continuous ...
f(10) = 100 , so 100 = m(10) + b

to be differentiable ...
f'(10) = 20, so 20 = m ... b = -100
It's actually differentiable to be continuous.

6. Originally Posted by Krizalid
It's actually differentiable to be continuous.
I agree ... I did not mean that as a continued statement.

It's just easier to start with continuity when trying to determine m and b.

7. Well thank you very much skeeter. That was really helpful and I appreciated.