Question

Question 2: 60 Marks The function fx)-x-2x3-5x2+12x -5 as four distinct roots, we want to determine the roots by means of Müller's method (2.1) Which option is false? (10) (1) f(x) x-2x3-5x 12x-5 has no singularities and no obvious symmetries and f(0)--5 (2) f(x) 4x3 6x2-10x 12, f(x) 12x2 - 12x (3) f"(x) has a local ertremum at X = 0.5 (4) the two zeros for f"(x) are -0.5408 and 1.5408 (5) f"(x) has a local marinum at X = 0.5 10 and x) 24x 12

Answer 1

given that f(x)=x⁴-2x³-5x²+12x-5

Let us take x₀=0,x₁=1,x₂=2

f(x₀)=(0)⁴-2(0)³-5(0)²+12(0)-5=-5

f(x₁)=(1)⁴-2(1)³-5(1)²+12(1)-5=1-2-5+12-5=1

f(x₂)=(2)⁴-2(2)³-5(2)²+12(2)-5=16-16-20+24-5=-1

2-2 2. ゾ↑ 36I6

-6-2 o)ss16-16-30424-5. -07a)-2(599)-3-2324)+ 308 5 I 154 -O-2153

(x) 12 1 10 locot enticmom Gfors) , 12(0-25)-6-10 ④ -len) a(, -o.su0g and 1. Suog 12 -10.