Question

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.

Answer 1

`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`