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

Answer:

$s'(t) = 21t^{2} - 2t$

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

Step-by-step 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

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

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

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

$s'(t)|_{t=9} = 1683$