For f (x) = x^5-x^3 x what is the equation of the tangent line at x=3?

F (x) = x^5 - x^3 + x

f' (x) = 5x^4 - 3x^2 + 1

f (3) = (3) ^5 - (3) ^3 + 3 = 243 - 27 + 3 = 219

f' (3) = 5 (3) ^4 - 3 (3) ^2 + 1 = 5 (81) - 3 (9) + 1 = 405 - 27 + 1 = 379

Let the required equation of the tangent line be

y = mx + c; where y = 219, m = 379, x = 3

219 = 379 (3) + c = 1,137

c = 219 - 1,137 = - 918

Therefore, required equation is

y = 379x - 918