The instantaneous rate of change is how much a function changes, at that a particular point
The instantaneous rate of change of f(x) at x =3 is [tex]-\frac{5}{3}[/tex]
The function is given as:
[tex]f(x) =x^3 - 6x^2 + 8x - 2[/tex]
And the point is given as:
[tex]x = 3[/tex]
The instantaneous rate of change (r) is calculated as:
[tex]r = \frac{f(x)}{x}[/tex]
So, we have:
[tex]r=\frac{x^3 - 6x^2 + 8x - 2}{x}[/tex]
Substitute 3 for x
[tex]r=\frac{3^3 - 6 \times 3^2 + 8\times 3 - 2}{3}[/tex]
[tex]r=\frac{-5}{3}[/tex]
Rewrite as:
[tex]r= -\frac{5}{3}[/tex]
Hence, the instantaneous rate of change of f(x) at x =3 is [tex]-\frac{5}{3}[/tex]
Read more about instantaneous rate of change at:
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