Question

Let g(x) = x2 − 5 x . First find the slope m of the line joining (1, g(1)) and (2, g(2)). Then use the Newton-Raphson method to estimate the values of c for which g'(c) = m. Check that your calculator is set for at least 10 digit display. Continue the process until successive iterations obtained by the calculator are identical

Answer 1

To find the slope of the line joining two points, calculate the values of g(1) and g(2) first. Then use the slope formula to find the slope. Finally, substitute the slope into the derivative of g(x) equation to find the values of c for which g'(c) = m.

Step-by-step explanation:

To find the slope of the line joining the points (1, g(1)) and (2, g(2)), we need to find the values of g(1) and g(2) first. Plugging in 1 into the function g(x), we have g(1) = 1^2 - 5(1) = -4. Plugging in 2 into the function, we have g(2) = 2^2 - 5(2) = -6. So the two points are (1, -4) and (2, -6).

Using the slope formula, m = (y2 - y1) / (x2 - x1), we have m = (-6 - (-4)) / (2 - 1) = -2.

Now, we need to find the values of c for which g'(c) = m. The derivative of g(x) is g'(x) = 2x - 5. Substituting m = -2 into the equation, we have 2c - 5 = -2. Solving for c, we get c = 1.5.