Problem solving Essay Examples

Problem Solving 1.a). Coordinates of points of inflection f(x)=e-x22f'(x)=(-x)(e-x22)Second derivative = e-x22+e-x22.x2it follows that when 0=e-x22(x2-1)x=±1f(1)=1√eThe points of inflections are (1, 1/√e) and (-1, 1/√e) b).f(x)=x+2sinxfirst derivative =1+2cos x Second derivative =2sinxGetting the local maxima and minima we equate the first derivative to zero 1+2cos x=0cos x=-12x=2π3, 4π3 evaluating the second derivative at x=2π3 and x=4π3-2sin2π3 =-2sin32=-√3. Therefore x=2π3 is a maximum value -2sin4π3 =-2sin-32=√3And x=4π3 minimum C. f(x)=x13(x+4)The first derivative =x13ddx(x+4)+x+4ddxx13=x13+(x+4)(13x23)=x13+(x3x23+43x23)f'(x)=43x23+4x133Using the...

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Problem Solving Part 1 V(t,x) =f(t)log(x+gty)+h(t) = =Vt-12(u-rδ)2VX2VXX+rxVX-βV+yVx+maxc-cVX+u1c=0=Vt-logu-rδVX2VXX +rxVX-βV+yVx+maxc-cVX+u1c=0Focusing on the time limit Such that Rearranginging Deviding by h Taking limits as h0 s.t The economic interpretation of g(t)y is labor income at the time, t. Part 2 2. 1. Optimal Trading Strategy Wealth process dXtπ=πtTμtdt+σtdWt+Xtπ-1nTπtX0=x0y=EβTI(βTST, where I is the optimal trading. where , and is uniquely determined by 2.2. Optimal Consumption in terms of X(t)+g(t)y= Such that,left952500 = Reference Bensoussan, A., & Zhang, Q. (2009). Mathematical modeling and numerical...