Home | 18.01 | Chapter 9 | Section 9.3

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If f is differentiable as well as continuous at the solution point, it looks like its tangent line near it.

Newton's Method calculates a new point by looking along the tangent lines while this method chooses the center of the previous interval as its new point.

Therefore, when you are within close range and f is close to its tangent line, Newton's Method homes in on the solution point much faster than this method does.