## Rates of Change? (3s^3 - s^2 + 5s) / (s^3 + 10), s = 1.5

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
Michael.Lu
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### Rates of Change? (3s^3 - s^2 + 5s) / (s^3 + 10), s = 1.5

Pre-Calculus apparantely so I thought it'd go here anyways

Rate of Change problem using the equation [f(a+h) - f(a)] / h to find the instantaneous velocity.

f(x) = (3s^3 - s^2 + 5s) / (s^3 + 10), s = 1.5

I need the slope of the tangent when s = 1.5

Can't use derivatives, says the teacher

nona.m.nona
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### Re: Rates of Change?

When using the expression for the instantaneous "slope":

$\frac{f(a\, +\, h)\, -\, f(a)}{h}$

...are you supposed to be taking the limit of the expression as $h\, \rightarrow \, 0\, ?$

(Whatever method you're supposed to use, I think the "point" of this exercise is to "convince" you of the usefulness of the Quotient Rule. This will involve some incredibly messy algebra!)