The position of an object at time t is given by s(t) = -4 - 2t. Find the instantaneous velocity at t = 6 by finding the derivative.

Question

anonymous · Answer

(f(a+h) - f(a)) / h

anonymous · Answer

the velocity is ds/dt. So, differentiate s(t) to get v(t) and then plug the value of t in the expression.

anonymous · Answer

how do i differentiate?

anonymous · Answer

$$\frac{ f(a+h) -f(a) }{ h}$$

anonymous · Answer

I don't think that makes any sense, which one would be f,a and h?

anonymous · Answer

when you differentiate the constant term will vanish. Any term like $$cx^n$$ will become $$ncx^{n-1}$$. Thus 2t will become $$1.2.t^0 = 2.1 = 2$$

anonymous · Answer

So once we differntiate, I just add/subtract and that'll be my answer?

anonymous · Answer

yes.

anonymous · Answer

rkopen has given you the shortcut to solving this problem. Do you understand

anonymous · Answer

-4-2 = -6 

So -6 is my derivative, correct?

anonymous · Answer

No -4 term will become 0 since 4 is a constant.

anonymous · Answer

0-2=-2?