Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)=2x^2 at x=3

Answer 1

f^'(3) = lim_x→3 (f(x) - f(3)) / (x - 3)

= lim_x→3 (2x² - 18) / (x - 3)

= lim_x→3 2(x + 3)(x - 3) / (x - 3)

= lim_x→3 2(x + 3)

= 12