How do you find the slope of a tangent line to the graph of the function f(x)=x^3-2x+1 at (2,5)?

Sep 21, 2016

$k = 10$

Explanation:

$\left({x}_{0} , {y}_{0}\right) = \left(2 , 5\right)$

$y = k x + n$
$k = f ' \left({x}_{0}\right)$

$f ' \left(x\right) = 3 {x}^{2} - 2 \implies f ' \left({x}_{0}\right) = f ' \left(2\right) = 10$

$k = 10$