# How to find instantaneous rate of change for f ( x ) = x <mrow class="MJX-TeXA

How to find instantaneous rate of change for $f\left(x\right)={x}^{2}+3x+4$ when x=4?
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Elianna Douglas
Explanation:
This is just the value of f'(x) at x = 4
f'(x) = 2x + 3
and f'(4) = 2(4) + 3 = 8 + 3 = 11
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Kapalci
Given:
${x}^{2}+3x+4,x=4$
$\frac{d}{dx}\left({x}^{2}+3x+4\right)=2x+3$
x=4
$\left(\frac{d}{dx}\left({x}^{2}+3x+4\right)\right){|}_{\left(x=4\right)}=\left(2x+3\right){|}_{\left(x=4\right)}=11$
$f\left(x\right)={x}^{2}+3x+4$ at x=4 is 1