Instantaneous and average velocity help

[showtimeballa]

vAn objects moves horizontally according to the following equation s(t)=t³-2t²-5t+6. Determine the instantaneous velocity of the object at t0=1 second using the definition of a derivative at a point.

v'(t)= lim (s(t₀+h)-s(t₀))/h
h-->0


And
What is the average velocity of the object from t=0 to t=2?
Average velocity= (s(t₂)-s(t₁))/(t₂-t₁)



For the first one, i got:
((1+h)³-2(1+h)²-5(1+h)+6-1³-2(1)²-5(1)+6)/h

I expanded and factored all of that ang got (h(-1+h+h²)/h then i plugged in 0 for h and got -1 as the instantaneous velocity... is that correct?

I got the first one... i just added the values wrong... i got -6. But i still don't know how to do the second one.

and for the second one, i have (3(2)²-4(2)-5)/2-0 but that makes it 0/2 and i know that this can't be.

Can you please help me?thank you!

 

[Pacopag]

For the second part, it looks like you used the derivative of s (i.e. the velocity) in the numerator. You should use s itself (i.e. plug t1 and t2 into s(t) for the numerator) as in the definition of average velocity.

 

[showtimeballa]

For the second part, it looks like you used the derivative of s (i.e. the velocity) in the numerator. You should use s itself (i.e. plug t1 and t2 into s(t) for the numerator) as in the definition of average velocity.

so it should just be (-4-0)/(2-0)=-1/2?

 

[Pacopag]

I think so. No. Wait a minute. Check it again. I think your t1 part is wrong. Just check it over carefully.

 

[showtimeballa]

wait wouldn't it be -5 for the average velocity instead?

 

[Pacopag]

Yeah. That's what I get.

 

[showtimeballa]

thank you!