Newton's method can be explained graphically by looking at intersections of tangent lines with the x-axis. First, a line tangent to the f at xn is calculated. Next, the intersection between this tangent line and the x-axis is found. Finally, the x-position of this intersection is recorded as the next guess, xn+1.
n uː t ə n z WORD_BOUNDARY m ɛ θ ə d WORD_BOUNDARY k æ n WORD_BOUNDARY b iː WORD_BOUNDARY ɛ k s p l eɪ n d WORD_BOUNDARY ɡ ɹ æ f ɪ k l i WORD_BOUNDARY b aɪ WORD_BOUNDARY l ʊ k ɪ ŋ WORD_BOUNDARY æ t WORD_BOUNDARY ɪ n t ə ɹ s ɛ k ʃ ə n z WORD_BOUNDARY ʌ v WORD_BOUNDARY t æ n d̠ʒ ə n t WORD_BOUNDARY l aɪ n z WORD_BOUNDARY w ɪ ð ð ɪ WORD_BOUNDARY ɛ k s æ k s ɪ s WORD_BOUNDARY f ɜː s t WORD_BOUNDARY ʌ WORD_BOUNDARY l aɪ n WORD_BOUNDARY t æ n d̠ʒ ə n t WORD_BOUNDARY t ə WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɛ f WORD_BOUNDARY æ t WORD_BOUNDARY ɛ k s ɛ n WORD_BOUNDARY ɪ z WORD_BOUNDARY k æ l k j ʊ l eɪ t ɪ d WORD_BOUNDARY n ɛ k s t WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɪ n t ə ɹ s ɛ k ʃ ə n WORD_BOUNDARY b ɪ t w iː n WORD_BOUNDARY ð ɪ s WORD_BOUNDARY t æ n d̠ʒ ə n t WORD_BOUNDARY l aɪ n WORD_BOUNDARY æ n d WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɛ k s æ k s ɪ s WORD_BOUNDARY ɪ z WORD_BOUNDARY f aʊ n d WORD_BOUNDARY f aɪ n ə l i WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɛ k s p ə z ɪ ʃ ə n WORD_BOUNDARY ʌ v WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ɪ n t ə ɹ s ɛ k ʃ ə n WORD_BOUNDARY ɪ z WORD_BOUNDARY ɹ ɪ k ɔ ɹ d ɪ d WORD_BOUNDARY æ z WORD_BOUNDARY ð ə WORD_BOUNDARY n ɛ k s t WORD_BOUNDARY ɡ ɛ s WORD_BOUNDARY ɛ k s ɛ n WORD_BOUNDARY p l ʌ s WORD_BOUNDARY w ʌ n WORD_BOUNDARY