Question

The position of an object time t is given by s(t)=7-14t . Find the instantaneous velocity at t=7 by finding the derivative.
Please explain!

Answer 1

@Hero

Answer 2

The derivative is the slope of the function. You can plug any x value into the derivative, and get the slope of the original equation at that point. Note: Instantaneous .... is a fancy way of saying find the slope!

Apply the chain rule since we have a linear equation.
s'(t) = -14
By the chain rule 7 goes to 0.
-14t^1 becomes 1 * -14t^(1 -1) = -14t^0 = -14.

This means that the instantaneous velocity at any point is the same.

Answer 3

So for example, in a problem like s (t)=-9-5t with t=4. I would use the chain rule with -5?

Answer 4

@Iamsinged