# Thread: rate of change

1. ## rate of change

a/find the instantaneous rate of change of $f(x)=x^2+3x+4$ when $x=2$

b/ find the average rate of change of $f(x)=x^2+3x+4$ between $x=2$ and $x=4
$

c/given $f(x)= \frac{1}{2x+1}$ and $g(x)=\sqrt{3x-5}$, determine (f.g)(x) and its domain

2. Originally Posted by william
a/find the instantaneous rate of change of $f(x)=x^2+3x+4$ when $x=2$

$\textcolor{red}{\lim_{x \to 2} \frac{f(x) - f(2)}{x-2}}$

b/ find the average rate of change of $f(x)=x^2+3x+4$ between $x=2$ and $x=4
$

$\textcolor{red}{\frac{f(4) - f(2)}{4-2}}$

c/given $f(x)= \frac{1}{2x+1}$ and $g(x)=\sqrt{3x-5}$, determine (f.g)(x) and its domain

$\textcolor{red}{(f \cdot g)(x)}$ or $\textcolor{red}{(f \circ g)(x)}$ ?
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3. Originally Posted by skeeter
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its $(f\circ g)$

4. Originally Posted by william
c/given $f(x)= \frac{1}{2x+1}$ and $g(x)=\sqrt{3x-5}$, determine $(f \circ g)(x)$ and its domain

corrected the composition notation

$(f \circ g)(x) = f[\textcolor{red}{g(x)}]= \frac{1}{2\textcolor{red}{(\sqrt{3x-5})}+1}$