Derive the 2nd order accurate finite difference approximation
for the 1st derivative of a function at the data point Xo. That is,
find the coefficients a, b, c such that: af(Xo) + bf(X1) + cf(X2) =
f'(Xo) + O(h^2). (Note: there is a prime sign on the f'(Xo) at the
right side)
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(−1)
The rule of the derivative of a function f is given. Find the
location of all local extrema.
f'(x) = (x2- 1)(x - 2)
Group of answer choices
Local maxima at -1 and 2; local minimum at 1
Local maximum at 1; local minima at -1 and 2
Local maximum at -1; local minima at -2 and 1
Local maximum at 2 - ; local minimum at 2 +
1. Solve the following below
A) Use the second derivative test to find all the local maxima,
local minima and saddle points of f(x,y)=x^2 +xy+y^2 +y
B) Find the absolute minimum and maximum values of f (x, y) =
x^2 + y^2 − 2x on the closed triangular region with vertices (2,
0), (0, 2) and (0, −2). [First find interior critical points, then
critical points on the boundary, i.e. on each edge of the triangle.
Finally, include the vertices...
Find the relative extrema, if any, of the function. Use the second
derivative test, if applicable. (If an answer does not exist, enter
DNE.)
g(x)=x^3-6x
relative maximum
(x, y) = (
, )
relative minimum
(x, y) = (
, )