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Differentiate the function and find the slope of the tangent line at the given value of the independent variable. s = 7t^3 -t^2, t = 9 s'(t) = ___ The slope of the tangent line is ___ at t=9.

User MeetM
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1 Answer

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Answer:


s'(t) = 21t^(2) - 2t

The slope of the tangent line is 1683 at t=9.

Explanation:

Given function s' = 7t³ - t²


s'(t) = (7 * 3)t^(3-1) -  (2 * 1)t^(2-1)


s'(t) = 21t^(2) - 2t

The slope of the tangent line at t = 9


s'(t)|_(t=9) = 21(9)^(2) - 2(9)


s'(t)|_(t=9) = (21 * 81) - 18


s'(t)|_(t=9) = 1701 - 18


s'(t)|_(t=9) = 1683

User Ebernie
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