Tentukan turunan fungsi berikut menggunakan rumus f(x) = lim h mendekati 0 f(x) = f(x+h) -f(x) /h A. F(x) = 4/3x^3 B. F(x) = 2x^3+6x^2-8

A. Menghitung turunan fungsi F(x) = 4/3x^3 menggunakan rumus f(x) = lim h mendekati 0 f(x) = [f(x+h) -f(x)] /h: f(x) = 4/3x^3 f(x+h) = 4/3(x+h)^3 Maka, f'(x) = lim h mendekati 0 f(x) = [f(x+h) -f(x)] /h = [4/3(x+h)^3 - 4/3x^3] /h = [4/3(x^3 + 3x^2h + 3xh^2 + h^3) - 4/3x^3] /h = [4/3(3x^2h + 3xh^2 + h^3)] /h = 4x^2 + 4xh + h^2 Maka, turunan fungsi F(x) = 4/3x^3 adalah f'(x) = 4x^2. B. Menghitung turunan fungsi F(x) = 2x^3+6x^2-8 menggunakan rumus f(x) = lim h mendekati 0 f(x) = [f(x+h) -f(x)] /h: f(x) = 2x^3+6x^2-8 f(x+h) = 2(x+h)^3 + 6(x+h)^2 - 8 Maka, f'(x) = lim h mendekati 0 f(x) = [f(x+h) -f(x)] /h = [2(x+h)^3 + 6(x+h)^2 - 8 - (2x^3+6x^2-8)] /h = [2(x^3 + 3x^2h + 3xh^2 + h^3) + 6(x^2 + 2xh + h^2) - 16] /h = [2x^3 + 6x^2h + 6xh^2 + 2h^3 + 6x^2 + 12xh + 6h^2 - 16] /h = [2h^3 + 6xh^2 + 12xh + 6] /h = 2h^2 + 6x + 12 Maka, turunan fungsi F(x) = 2x^3+6x^2-8 adalah f'(x) = 6x^2 + 12x.