Question

evaluate the derivative of the following function at the given point. f(t)=2t^2 - 4t, a = - 1
f(-1)= (type an integer or a simplified fraction.)

Explanation:

Step1: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $f(t)=2t^2-4t$, the derivative of $2t^2$ is $2\times2t^{2 - 1}=4t$ and the derivative of $-4t$ is $-4\times1t^{1 - 1}=-4$. So, $f^\prime(t)=4t - 4$.

Step2: Evaluate the derivative at $t=-1$

Substitute $t = - 1$ into $f^\prime(t)$. We get $f^\prime(-1)=4\times(-1)-4$.
$f^\prime(-1)=-4 - 4=-8$.

Answer:

$-8$