Question

use the definition of the derivative to find the derivative of: $f(t)=-3 - 6t$. $f(t)=$

Explanation:

Step1: Recall derivative definition

The definition of the derivative of a function $y = f(t)$ is $f^{\prime}(t)=\lim_{h
ightarrow0}\frac{f(t + h)-f(t)}{h}$.

Step2: Find $f(t + h)$

Given $f(t)=-3-6t$, then $f(t + h)=-3-6(t + h)=-3-6t-6h$.

Step3: Substitute into derivative formula

$\frac{f(t + h)-f(t)}{h}=\frac{(-3-6t - 6h)-(-3-6t)}{h}=\frac{-3-6t-6h + 3+6t}{h}=\frac{-6h}{h}=-6$.

Step4: Take the limit

$f^{\prime}(t)=\lim_{h
ightarrow0}\frac{f(t + h)-f(t)}{h}=\lim_{h
ightarrow0}(-6)=-6$.

Answer:

$-6$