Question

section 2.4: power and sum rules for
score: 50/180 answered: 5/18
question 6
let (f(x)=-2x + 6).
then (f(2)=)
and after simplifying (f(x)=)

Explanation:

Step1: Apply power - sum rule for differentiation

The power rule states that if $y = ax^n$, then $y'=nax^{n - 1}$, and for a constant $c$, $(c)' = 0$. Given $f(x)=-2x + 6$, where $a=-2,n = 1$ for the first term and $c = 6$ for the second term. So $f'(x)=-2\times1\times x^{1 - 1}+0$.

Step2: Simplify $f'(x)$

$f'(x)=-2$.

Step3: Find $f'(2)$

Since $f'(x)$ is a constant function ($f'(x)=-2$ for all $x$), then $f'(2)=-2$.

Answer:

$f'(2)=-2$
$f'(x)=-2$