Let a < b and let f(x) be a continuously differentiable function on the interval [a, b] with f(x) > 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = is given by y(x) [* dx ƒ(x) √ 1 + y^², _y(a) = A₁ y(b) = B, A, a = A+B 1² d dw 1 √f (w)² - 3² where is a constant satisfying b B-A= B 3 [º a 1 √f(w)² - 32 Using the Jacobi equation, show that the stationary path gives a weak local minimum of the functional S[y]. dw

Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: Let h be a differentiable function with a tangent line at x = TT. The equation of the tangent line…

A: We have to find the value of h(x) at x=0,π

Q: Use implicit differentiation to find and .Assume that the equation defines z as a differentia ôy…

A: The given equation is; x4y4z=sin(7x+5y+2z)

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: let f be a function whose derivative is given by f'(x)=( x/15) +sin(e^0.2x) . How many relative…

A:

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

A:

Q: Let f and g be functions differentiable on R. with Find f(x)|x=2= d g(2) = 2, 9(x)\x=2 = 4, de…

A:

Q: 2. Let f(x) be a function with domain (00, -00) and f'(x) = 2x3+3x²-36r. Find the intervals where…

A: Step 1:Step 2: Step 3: Step 4: