Question

question 3
if $f(x) = 23x + 25$, find $f(-8)$.
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question 4
use the limit definition of the derivative to find the instantaneous rate of cha
$f(x) = 7x^{2} + 7x + 4$

Explanation:

Step1: Apply power rule to derivative

For $f(x)=23x+25$, derivative rule: $\frac{d}{dx}(kx^n)=knx^{n-1}$, $\frac{d}{dx}(c)=0$.
$f'(x)=\frac{d}{dx}(23x)+\frac{d}{dx}(25)=23x^{1-1}+0=23$

Step2: Evaluate $f'(-8)$

The derivative is constant, so substitute $x=-8$.
$f'(-8)=23$

Answer:

23