f(x) = (x + 4)^2 - 3 = x^2 + 8·x + 13
f'(x) = 2·x + 8
Tangente durch einen Punkt
f(x) = f'(x) * (x - 1) + 1 --> x = 1 ± √21
f'(1 + √21) = 2·√21 + 10
f'(1 - √21) = 10 - 2·√21
t1(x) = (2·√21 + 10) * (x - 1) + 1 = 19.17·x - 18.17
t2(x) = (10 - 2·√21) * (x - 1) + 1 = 0.8348·x + 0.1652
Skizze
~plot~ (x + 4)^2-3;19.17x-18.17;0.8348x+0.1652 ~plot~