7. Given f"(x) = T a. Find the interval(s) of r where f is concave up; b. Given r = -2 is a critical point of f (i.e. f'(-2) = 0), docs f have a maximum or minimum at -2? Is it a local one or global one?

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

A:

Q: For what values of the constant k does the Second Derivative Test guarantee that f(x.y)=x+kxy+y will…

A:

Q: 1. Ta)Galculate the critical polnts of Hhe function z(x, y) = K-1} + (q-3) - 5, subjet to %3D X +2y…

A:

Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: (1) Use the linear approximation of Va at x = 9 to estimate the value of v8.7

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Show that f(x, y) = x^2 + y^2 − 2xy + 4 has infinite number of critical points and that D = 0 at…

A: Given that      f(x,y) = x2+y2 -2xy+4 has infinite number of critical points and D= 0 at each one.…

Q: 1- Find the derivative of ywith respect to x, t, or 0 as appropriate + 5. y = In 3x 6. y = In kx, k…

A: Derivative of the function

Q: Using a local linear approximation of f(x) = v4 + x at a 0 to estimate the value of v4.3 gives

A:

Q: What is the isogonal trajectories cutting at angle of 0= arctan 4 to the family of curves whose…

A:

Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

A: .

Q: 2) For each of the IVPS sin (t) + 2y dt dy (2.1) t- 5) = dy (2.2) t - y = 0, y(1) = yo > 0, dt t >0,…

A: Fundamental theorem of existance and uniqueness of solution: Consider the initial value problem…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 8y < 8. 1. Absolute minimum of f(x, y) is…

A:

Q: (1) Let f(r, y) = (x + y)e-=v. a) Determine the quadratic approximation function of f(r, y) at the…

A:

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: 4-The area bounded by the curve y = 2x- r and the x- axis is 5- if y = x - 2r +4 and x = t +2 then…

A:

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: ----j n(x, y) = x² + 3xy – 6y has a critical point at (2,- Use the second derivative test to…

A:

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x&gt;0

Q: 1 Find the local linear approximation of f(x) = , at 3+ 1 Tg = 2, where Az = I- 2. NOTE: Enter the…

A:

Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical…

A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

A:

Q: Suppose f(x, y) = x² + y? – 2x – 4y +5 (A) How many critical points does f have in R?? 1 (B) If…

A: The given function is fx,y=x2+y2-2x-4y+5 Compute the critical points as follows.…

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

A:

Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

Q: 5. Suppose f is twice differentiable at xo. If f'(xo) = 0 and f"(x,) > 0, then (a) f has relative…

A: As we know if f(x) is continuous in the domain then and there is a point x= a exist such that

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

A:

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

A:

Q: 9. Find the critical points and classify these as local max, local min, saddle point, or "can't…

A: (f) . Given function psf(x,y,2 = (x2+2y2+322)e  (x2+y2+22)solution :-To find the critical pointsfx =…

Q: (3) (a) Find the local linear approximation of f(x) = /1+x at xo = 0. Use your approxima- tion…

A:

Q: Let f(x, y) be a function and (a, b) be a critical point of f . Given that (a, b) is a saddle point…

A:

Q: 4.2) Suppose you wanted to find the absolute extrema of f(x, y) = ax² + bxy+cy? + dx + ey on the…

A: The given function is, fx,y=ax2+bxy+cy2+dx+ey We have one critical point on the rectangle,…

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

A:

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: What are the critical points of the function f (x, y) = cosh(x + 1) + sin(ry)– ex+1)y on the line y…

A:

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

A:

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

A:

Q: 10. Find the minimum of the integral I[y] subject to the constraint TIy) = [, s° dx = 2 JL over all…

A: Consider the problem: Extremize I[y]=∫x1x2F(x, y, y') dx subject to J[y]=∫x1x2G(x, y, y') dx=L ,…

Q: none 1 point The y-intercept of the tangent line to the aurve of y = Vx +3 at the point (1, ) is…

A: