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Functions : Increasing, Decreasing and Extrema

Please explain and express the answer exactly, for example √3 rather than in decimal form, thanks:

s(t) = -8t^9 + 9t^8 - 7

(a) Where is the function increasing?
(b) Where is the function decreasing?
(c) Where does the function have local maxima?
(d) Where does the function have local minima?

(^ means exponent)

Solution Preview

Please explain and express the answer exactly, for example √3 rather than in decimal form, thanks:

s(t) = -8t^9 + 9t^8 - 7

(a) Where is the function increasing?

Solution. As s(t) = -8t^9 + 9t^8 - 7 , by taking derivative, we have

s'(t) = -72t^8 + 72t^7
...

Solution Summary

Areas of increase and decrease and extrema for a function are found.

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