Please solve this problems manually

course: numerical method -control system engineering

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Apply two iterations of the Secant Steepest Accent Method the find the optimum. f(x)=x227x+12+y2 Starting with the initial points (2,2) Appendix: Secant Steepest Accent Steepest Ascent Method Algorithm a) Start from initial point (x0,y0) b) Calculate the gradient xf,yf (Best direction ) c) Calculate g(h), a function of a vector along the gradient direction g(h)=f(x0+xfh,y0+yfh) d) Calculate g(h) to find h that have the maximum along g(h) e) Transfer h back to (x1,y1) (x1,y1)=(x0+xfh,y0+yfh) Consider the following function: f(x)=x42x38x25x With the interval [2,1]. a) Use analytical methods to show the function has an optimum for some value of x in the range of [2,1] (i.e. using differentiation ) b) Check if the optimum is a maximum or minimum (sign of f(x) ) c) Employ the Golden-section search to find the maximum of the function f(x) (three iterations, XL=2,Xu=1 ) and complete the table Appendix: Golden-Section Search Algorithm - Choose two points x1,x2 in the interval [x1,xu] x1=xl+0.618034(xuxl) x2=xt+0.381966(xuxt) -if f(x2)f(x1) - The maximum cannot be between xH ane xu=x1 x1=x2 -Repeat until Xuxt