Answer to Question #332130 in Algorithms for Jaguar

Question

Consider now the function f(x) = x^4−2x^3 − 12x^2 + 16x − 4 which has four distinct roots.

Question 8

Which of the following options is FALSE?

(1) f'(x) has a local minimum at 2.

(2) f'(x) has a local maximum at −1.

(3) f(x) has no singularities and no obvious symmetries and the y-intercept is −4.

(4) f"(x) has a local maximum at x = 0.5.

(5) the two zeros of f"(x) are −1 and 2.

Question 9

Which of the following results is FALSE when applying the various methods as indicated:

(1) p = 0.88338140 when applying the secant method with starting points p0 = 0 and p1 = 1.

(2) p = 0.34170924 when applying the bisection method with the starting points p0 = 0 and p1 = 1.

(3) p = 0.34170924 when applying Newton’s method with starting point p0 = 0.

(4) p = 0.88338140 when applying Muller’s method with starting points p2 = 0, p0 = 1 and p1 = 5.

(5) p = 4.04823531 when applying the regula falsi method with starting points p0 = 1 and p1 = 5.

Answer 1

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