What is the instantaneous rate of change of $f(x)=sqrt(3x^2+4x+2)$ at $x=4$ ?

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Answer 1 · 2016-04-05T21:43:45

$f'(4)=28/(2sqrt66)=1.72328$ .

The instantaneous rate of change at a point is equivalent to the derivative evaluated at that point.
We evaluate this derivative by using the power rule.

$therefore f'(x)=d/dx(3x^2+4x+2)^(1/2)$

$=1/2(3x^2+4x+2)^(-1/2)*(6x+4)$

$therefore f'(4)=(6(4)+4)/(2sqrt((3(4^2)+4(4)+2)))=28/(2sqrt66)=1.72328$ .

What is the instantaneous rate of change of f(x)=sqrt(3x^2+4x+2) f(x)=sqrt(3x^2+4x+2) at x=4 x=4 ?