Consider the Secant Method applied to minimising f(x) = x² + x³ in |x| < 1. We know the minimiser is x* = 0, but let's derive that the order of the method is here p = 1.6180. Question 1 Substituting the function into the Secant Method gives which of the following iterations? O #k+1 #k+1= k+1 = Oak+l (3+2+2x-1) 3(x+1)+2(x+2-1+₁) 1+22 3+42 6(1+) 21 1+2+2-1

The Complementary Function for (D – 14)²y = 0 is _ None 100a Ye = (C1 + C,x)el00z Yc = (C1 + C2x)el4z Ye = (C1 + Czx)e 14z

3. If f(x) = kx³ -1 and f¹(15) = 2, find k_

to STUDENTS of 5さ WHAT FUNCTION =C(x) =

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Bb Tangipahoa Parish School Sys X OnCourse Connect &Asses. b oncourseconnect.com/assessment/1438899/14a98249-ae A TPSS Bookmarks (2/1/2021) MCCR BLITZ_FUNCTIONS (RESUMED) ALGEBRAII 28-2 (AARON JAMES, ID: 12390724) 3. Given that f(x) = -x + 6 and g(x) = x what is the value of f (g(-3))? Hint: Work the problem from the inside out. Meaning 1. find g(-3) by plugging in -3 into th A -12 B 0. 12 24 ()

3 Suppose f(x) = 47rx2e-x - e-* for all x E R. Show that f= -f. %3D

3. Consider a single node x0 and stepsize h. Based on these answer the following:(Q) Derive the formula for Forward Difference method of numerical derivative and show how theerror is related to the stepsize h.

10) Find (¹)(3) if f(x)=x²+x-1.

Please Show Each and Every Working VERY CLEARLY. There are NO multi-questions here, only just multi-PART questions which are CONNECTED to each other, and hence, Please do NOT Leave any, Thank You! verify