How do you find the equation of a line tangent to the function y=x^3+6 at (1,7)?

Nov 7, 2016

$y = 3 x + 4$

Explanation:

The tangent equation is

$y - f \left({x}_{0}\right) = {f}^{'} \left({x}_{0}\right) \left(x - {x}_{0}\right)$

Then $f \left({x}_{0}\right) = 7 , {f}^{'} \left(x\right) = 3 {x}^{2} , f ' \left({x}_{0}\right) = {f}^{'} \left(1\right) = 3$ so the tangent is

$y - 7 = 3 \left(x - 1\right)$

$y = 3 x + 4$