The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x) =0 with initial approximation x1 =6 (a) Draw the tangent lines that are used to find x2 and x3 and estimate the numerical values of x2 and x3 . (b) Would x1 =8 be a better first approximation? Explain.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x) =0 with initial approximation x1 =6
(a) Draw the tangent lines that are used to find x2 and x3 and estimate the numerical values of x2 and x3 .
(b) Would x1 =8 be a better first approximation?
Explain.
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