Show that if 0 < μ < 2-r has a unique relative extreme (max) value for...

Question

Question

Answer 1

Answer #1

Any query then comment below..

For maxima , we firstly find critical point by taking first derivative equal to 0...then show that second derivative is negative..

2 2. Now as

Here we see that when value of nu is between 0 and 2 ... Then second derivative is maximum at x= 1/2 ...and this extreme value of x lies in (0,1) ..

So our result is proved

Answer 2

Similar Homework Help Questions

Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem...

Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).
2.10.4 Given a function f(x,y) on a compact region E in R^2, Find the maximum and...

2.10.4 Given a function f(x,y) on a compact region E in R^2, Find the maximum and minimum values of f on E, and the points at which these extreme values are attained. f(x, y) = x2 sin y + x, and E is the filled rectangle where -1 < x < 1 and | 0 < a < .
. c) + < 2 b) 2 + 3x 27, 0. Solve for r: r' +...

. c) + < 2 b) 2 + 3x 27, 0. Solve for r: r' + 2.r < 2.1? +12

Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle...

Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
9. IfX is a r.), distributed as N(μ, σ2), find the value of c (in terms...

9. IfX is a r.), distributed as N(μ, σ2), find the value of c (in terms of μ and σ) for which P(Xc 2-9P(X > c).
Show that ze?-? = cosz has one solution on {2EC:[2]<1}, and the solution is real number.

Show that ze?-? = cosz has one solution on {2EC:[2]<1}, and the solution is real number.

2. A charge distribution with spherical symmetry has density PoR (1) for 0< R< a, and...

2. A charge distribution with spherical symmetry has density PoR (1) for 0< R< a, and is zero for R spherical variable. Determine a. Here po and a are constants, and R is the (a) (20 points) E everywhere. (b) (20 points) the potential, V, everywhere.
2. Solve the initial-boundary value problem 2% for 0 < x < 6, t > 0,...

2. Solve the initial-boundary value problem 2% for 0 < x < 6, t > 0, u(0,t) = u(6,t) = 0 for t > 0, u(x,0) = x(3 - x) for 0 5736. (60 pts.)
7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n...

7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n >0 in probability if nP(Xn > n) -» 0. (b) Find a random variable Y satisfying nP(Y > n) ->0 and E(Y) = Oo

5. Let S be a non-empty bounded subset of R. If a > 0, show that...

5. Let S be a non-empty bounded subset of R. If a > 0, show that sup (aS) = a sup S where aS = {as : s E S}. Let c = sup S, show ac = sup (aS). This is done by showing: (a) ac is an upper bound of aS. (b) If y is another upper bound of aS then ac < 7. Both are done using definitions and the fact that c=sup S.