5

3. Let f(z.y) = IOO(y 2)2+(1-1)2 This is the famed banana funetion (see wikipedia) . The minimum of f is (1,1) (why?) Starting at the point (4,4) use a fixed step s...

Question

3. Let f(z.y) = IOO(y 2)2+(1-1)2 This is the famed banana funetion (see wikipedia) . The minimum of f is (1,1) (why?) Starting at the point (4,4) use a fixed step size to locate the minimum Here; since we are minimizing; YOur direction should be d) CV f(6)) How many iterations before YOu find the minimm? Starting at the point (4, 4) use steepest descent with back- tracking to find" the minimum;_ How many iterations be- fore YOu find the mininum? Use the R function nlm to find the minimm sta

3. Let f(z.y) = IOO(y 2)2+(1-1)2 This is the famed banana funetion (see wikipedia) . The minimum of f is (1,1) (why?) Starting at the point (4,4) use a fixed step size to locate the minimum Here; since we are minimizing; YOur direction should be d) CV f(6)) How many iterations before YOu find the minimm? Starting at the point (4, 4) use steepest descent with back- tracking to find" the minimum;_ How many iterations be- fore YOu find the mininum? Use the R function nlm to find the minimm starting at (4,4). How many iterations? Compare t0 (a) and (6).



Answers

After differentiating and setting the result equal to zero, many practical max-min problems lead to an equation that cannot be solved exactly. For the following problems, use a numerical method to approximate the solution to the problem. An object thrown from the edge of a 42-foot cliff follows the path given by $y=-\frac{2 x^{2}}{25}+x+42$ (Figure 10 ). An observer stands 3 feet from the bottom of the cliff. (a) Find the position of the object when it is closest to the observer. (b) Find the position of the object when it is farthest from the observer.

Hello, everyone. Today we're going to solve a problem. Number 13. Here you and function. If is it's plus why plus that plus Okay, so which is subject to affect its come over commas. Commodity is equal toe extra square plus y squared plus X square plus beef Quit So greeting f you go toe one comma, one comma, one come out one Creating these equal do two x comma toe comma toe the comma toe So one week or two laughter two weeks when we called toe lab there to buy when they called tow land. Or does that one nickel toe longer toe pick. Then one by land, I kowtow. So that's equal to toe. Equal toe tickle toe So x square Plus why square pleasure square, plus the square for excess square record toe one exact or two the ser minus one by which is equal toe. Why logistical does that which is equal toe pick so affect one day toe column on day two, one by one by toe, equal toe to, in fact minus one day too minus one day too minus one Graito minus one were toe equal toe minus street. This is maximum. This is minimum. So these are the solutions that

Today we're going to solve a problem. Number five here little functions with arguments. So creating tough function. If a technical on white equal to minus two, it cannot do what Great aunt off Jeep at X command by equal to expedite toe coma doorway So great interest Equal toe lambda the so minus two It karma, right Which physical toe? Lambda and do X right toe coma. Too late minus to execute toe, Explain to minus two Xa Kowtow Land index by two Then why you called land back to what? So minus two it's equal Tow land Exabyte two I'm di kowtow minus four To where you got toe minus four Start toe white by equal toe zero so active square My fault less life were equal to one extra square by four physical toe one This life where it's square by four equal to one exa kowtow foot Execute off this or my has to So my enough to call a zero And it two comma zero r potential extra money. Yeah. Thank you

But if you're going to solve problems, think here, go find extremely lists off. Ever mix like subject to country, you have X like equal to keep so dealt off. Ffx fight equal tow land. Other stuff Deals X Come on by gee off excrement by equal to kick. So 1/4 X come on white equal to it's square that's very square. The off X canal by equal to X y equal toe one full effects Equal toe Lambda GXE to execute toe Remember, but the question What f y equal toe Lamba achieve I very equal toe Lambda x two in tow, X plus y equals tow land dyinto X plus y landry Kowtow to so sub student equation When they get executed. Toe Right ridicules the two solution plus so minus one common plus or minus smart. So act plus or minus one plus or minus one. Yes, it could tow plus or minus one. The whole square, plus wrestle minus one. The whole square but difficult. Little X has no maximum value because limit ex common bite and took infinitely comma. Zero. Air Force X come out white according limit X come away tends to infinitive. Comma zero X squared plus y squared equals infinity. Thank you

Today we're going to solve problem number 11 Very difficult. Two X comma toe comma Does it then Delta Z Equal toe for X Cube Color for the Cube coma for the Cube. Then we have two x A kowtow lambda in the four x cubed two vehicle Tow lamb dyinto for y cube, too radical Toe lambda in tow for the Cube. So one bite two X squared equal to one day to live equal toe. One by does that square one. But X squared equals one by y squared equals one. By that square they get execute. Why equal toe that pointed for Wrote off one by three comma for throat off one by three Come on for throat off one by three. So it's a like existed for let's access to four. Plus access to four equal to one three expressed four equal to one excess tickle toe for throat off one by three out execute toe for truth off one by three. They get both won by three people to white equal toe that so ethic fall through it off one by three comma off one by three Coma Sort off one by three Pickle toe we got, like three in the off one by three, which is equal to fruit tree, so to execute. Tow land dying for X cube toe Goto landline for way cube. So the tickle toe lambda in tow for the cube so at X equal to zero and why you go to zero. They help zero rested for plus they're arrested for. Plus, they're dressed for equal to one. The decor toe the serve minus one, then to Mexico toe lambda in the four x cubed. So why you called Lambda in for y Cube so that they kowtow Lambda in tow for that cuba, So the possible points are zero comma, zero comma, plus or minus one zero comma comma zero plus or minus mint zero zero So effect zero comma zero comma. Let's not minus one equal toe zero square, zero square first plus or minus one. The whole squad, which is called what actual if a little three like one by three for truth off one by three for truth off one by three Minimum, it's one at zero comma, zero plus or minus one little come up, plus or minus +10 That's R minus 10 Comma zero. Thank you


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