find f(x) for the following function. then find f(3), f(0), and f(-4). f(x)=2x^2 - 10x f(x)=

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $f(x)=2x^2-10x$, the derivative of $2x^2$ is $2\times2x^{2 - 1}=4x$ and the derivative of $-10x$ is $-10\times1x^{1 - 1}=-10$. So, $f^\prime(x)=4x - 10$.

Step2: Find $f^\prime(3)$

Substitute $x = 3$ into $f^\prime(x)$: $f^\prime(3)=4\times3-10=12 - 10=2$.

Step3: Find $f^\prime(0)$

Substitute $x = 0$ into $f^\prime(x)$: $f^\prime(0)=4\times0-10=-10$.

Step4: Find $f^\prime(-4)$

Substitute $x=-4$ into $f^\prime(x)$: $f^\prime(-4)=4\times(-4)-10=-16 - 10=-26$.

Answer:

$f^\prime(x)=4x - 10$, $f^\prime(3)=2$, $f^\prime(0)=-10$, $f^\prime(-4)=-26$