find the value of the derivative of the function at the given point. f(x)=4x^2 - 2x; (-1,6) f(-1)=□ (type an…

Explanation:

Step1: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $f(x)=4x^{2}-2x$, the derivative $f^\prime(x)$ is: $f^\prime(x)=\frac{d}{dx}(4x^{2})-\frac{d}{dx}(2x)$. Using the power - rule, $\frac{d}{dx}(4x^{2}) = 4\times2x^{2 - 1}=8x$ and $\frac{d}{dx}(2x)=2\times1x^{1 - 1}=2$. So, $f^\prime(x)=8x - 2$.

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

Substitute $x = - 1$ into $f^\prime(x)$. $f^\prime(-1)=8\times(-1)-2$. $f^\prime(-1)=-8 - 2=-10$.

Answer:

$-10$