Question

The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t = 8 by finding the derivative.

Answer 1

Hello! There are a few ways to find the derivative. One famous formula is below:

Note, t = x = 8

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

To find the derivative of s(t) = -9 - 3t let insert it into our formula:

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

$\frac{(-9 - 3(x + h)) - (-9 - 3x)}{h}$

Insert x = 8

$\frac{(-9 - 3(8 + h)) - (-9 - 3(8))}{h}$

Do the Math

$\frac{(-9 - 3(8 + h)) - (-9 - 3(8))}{h}$

$\frac{(-9 - 24 - 3h)) + 9 +24)}{h}$

Group Like Terms

$\frac{-9 + 9- 24 +24 - 3h )}{h}$

Cancel Terms and Finish Doing The Math

$\frac{-9 + 9- 24 +24 - 3h )}{h}$

$\frac{ -3h }{h}$

$\frac{ -3h }{h} = -3$

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So when t = 8 the instantaneous velocity = -3