Find all points
(
x
,
y
)
where
f
(
x
,
y
)
has a possible relative maximum or minimum.
f
(
x
,
y
)
=
2
x
3
+
2
x
2
y
−
y
2
+
y
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
2.
Find the maximum point of y = x + =
a. (2,3)
b. (1,2)
c. (-1,-2)
d. (2,3)
We know that f(x, y, z)= x³- 9x² + y² + z² +24x-4z +20. Determine the optimum value of the function f(x, y, z) and state that the optimum value is the maximum or minimum value.
Find all local maximum and minimum points of ƒ = 2x² − xy + y² − 5x + 6y – 9.
Chapter 7 Solutions
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