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what is the average rate of change of y with respect to x over the interval { 1,5} for the function y=4x+2?
choices:
8
1/4( wrong)
2
4

- anonymous

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- Haseeb96

differentiate both sides of this function with respect to x
|dw:1436163187408:dw|

- Haseeb96

now dy/dx is showing speed

- anonymous

oh that makes more sense I see what id id wrong lol

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## More answers

- Haseeb96

in order to find average rate of change during the interval { 1,5}
we use this formula

- Haseeb96

|dw:1436163315029:dw|

- anonymous

can you help me with two more uestions I have tried answering them and keep getting them wrong.

- Haseeb96

okay
tag me
there

- Haseeb96

if you like my explanation click at best response

- anonymous

the height ,s , of a ball thrown straight down with initial speed 64ft/ sec froma cliff 80 ft. high is s(t)=-16t^2-64t+80, where t is the time elapsed that the ball is in the air. what is the instantaneous velocity of the ball when it hits the ground?
256
-96
0
112

- anonymous

evaluate lim x->2 f(x) for f(x)= |dw:1436163800477:dw|

- myininaya

average rate of change of y respect to x over the interval [1,5]
is
\[\frac{f(5)-f(1)}{5-1} \text{ where} f(x)=4x+2\]
or since f(x)=4x+2 is just a line you could use the slope of this line to determine the average rate of change over any given interval

- myininaya

to find velocity just differentiate the position function

- myininaya

but you will have to find when s=0 first

- myininaya

since it wants to know the velocity when it hits the ground (means height is 0 there so that is why we set s=0)

- myininaya

for the last one you will need to consider the left and right limits

- Haseeb96

|dw:1436164260135:dw|

- anonymous

what bout 2 and 3?

- myininaya

well have you solved s=0 yet?

- myininaya

and then differentiated s to find v

- anonymous

I got 80

- myininaya

how did you 80 from solving the equation s=0

- myininaya

\[-16t^2-64t+80=0 \\ \text{ you could divide both sides by -16 } \\ t^2+4t+5=0\]
can you see if you can solve that?

- myininaya

now this will tell us the value t such that s=0

- myininaya

s=0 means the height=0
we want to find t such that when this happens
so we can find the velocity when the ball hits the ground

- anonymous

oh ok

- myininaya

oops t^2+4t-5=0

- Haseeb96

is it -196 ?>

- myininaya

have you solved for t yet?

- anonymous

not one of my choices for number 2

- myininaya

I don't know if you still need help or not...

- anonymous

I don't have an answer for number 2 or 3 lol I have tried everythig

- myininaya

have you actually tried solving the equation I have asked you to yet/

- myininaya

and then differentiating the position function
to find the velocity function
and then entering the number you found from solving s=0 into velocity function to find the velocity when the ball hits the ground

- anonymous

yes and I am getting big numbers im terrible at it.
this is hwat I got- -96 is that right?

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