Question

Determine the global extrema of the multivariable quadratic
function: f(x,y)=ax^{2}+2bxy+cy^{2}

Answer #1

Determine where the given quadratic function has an extrema, and
then enter the coordinates of the vertex.
f(x) = 2x2 + 12x - 3
The function has a maximum or minimum value when x = __________.
The value of y at this point is__________?

Use a system of linear equations to find the quadratic
function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using
matrices.
f(1) = 3, f(2) = 12, f(3) = 25
f(x) =

quadratic function is a function of the form
y=ax2+bx+c where a, b, and c are constants. Given any 3
points in the plane, there is exactly one quadratic function whose
graph contains these points.
Find the quadratic function whose graph contains the points (5,
45), (−3, 5), and (0, 5).
Enter the equation below.

Find the global extrema of the function f(x) = (x^2 -
1)^1/3 on the interval [-1,2]

Consider the quadratic function f, given by f(x) = −x2 + 6x−8.
(i) Determine if the graph of y = −x2 + 6x − 8 is concave up or
concave down, providing a justiﬁcation with your answer. (ii)
Re-write the equation of the quadratic function f, given by f(x) =
−x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the
square. Hence determine the vertex of the graph of y = f(x).
(iii) Identify the x-intercepts and y-intercept...

Determine the global extreme values of the function
f(x,y)=2x3+2x2y+2y2,x,y≥0,x+y≤1
fmin=
fmax=

find the values of a,b and c for the quadratic polynomial f(x)=
ax2+bx+c which best fits the function h(x)=w^2x+1 at
x=0
f(0)=h(0), and f'(0)=h'(0), and f''(0)=h''(0)
check your answer by graphing both f and h on www,desmos.com and
zoom in around x=0. Explain what you notice.

Find the local extrema of the following function. f(x,y) =
x3-3xy2+15y2

Let f(x) be a quadratic function such that f(0)=−6 and
∫f(x)x2(x+5)7dx Determine the value of f′(0).

Find the domain of the multivariable function
((x^2*y^3)-(y^2+x^2-1)^3))^.5

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