Find all points ( x , y ) where f ( x , y ) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f ( x , y ) at each of these points. If the second-derivative test is inconclusive, so state. f ( x , y ) = 8 x y + 8 y 2 − 2 x + 2 y − 1
Find all points ( x , y ) where f ( x , y ) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f ( x , y ) at each of these points. If the second-derivative test is inconclusive, so state. f ( x , y ) = 8 x y + 8 y 2 − 2 x + 2 y − 1
Solution Summary: The author explains that the function f(x,y)=8xy+8+y2-2x+2y-1 has a possible relative maximum or minimum, and the nature of
Find all points
(
x
,
y
)
where
f
(
x
,
y
)
has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of
f
(
x
,
y
)
at each of these points. If the second-derivative test is inconclusive, so state.
f
(
x
,
y
)
=
8
x
y
+
8
y
2
−
2
x
+
2
y
−
1
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 .
3. Let f(x) = 8x- 3x*+5
%3!
a) Find where f has stationary points.
b) Perform a sign analysis on the derivative of f. Find where f is increasing and decreasing.
c) Use your results to find where all local maxima and minima of foccur.
Let f(x) = x³ = x² +
+ 28x. Locate any critical points for f. Then use
the First Derivative Test to determine whether they correspond to local maxima or local
minima.
Consider the function f(x) = In (x² - 4)
a.) Use the First Derivative Test or the Second Derivative Test to find any points that are local maxima and local minima. Include both x and y coordinates.
b.) Find any inflection points of f. Make sure to include both x and y coordinates.
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