Answer
The value of the derivative is: $\lim \limits_{h \to 0}(2.8t+1.4h)$, which equals to $2.8t$
$S'(-1)=2.8\times -1=-2.8$
Work Step by Step
The algebraic definition of a derivative can be written as:
$S'(t)=\lim \limits_{h \to 0} \frac{S(t+h)-S(t)}{h}$
By substituting the given function we get:
$\frac{S(t+h)-S(t)}{h}=\frac{1.4(t+h)^2-(1.4t^2)}{h}=\frac{1.4t^2+2.8th+1.4h^2-1.4t^2}{h}=\frac{2.8th+1.4h^2}{h}=2.8t+1.4h$
The value of the derivative is: $\lim \limits_{h \to 0}(2.8t+1.4h)$, which equals to $2.8t$
$S'(-1)=2.8\times -1=-2.8$
