Answered: Vf Vf B g(x, y) = 0 g(x, y) = 0 FIGURE…

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Calculus

Vf Vf B g(x, y) = 0 g(x, y) = 0 FIGURE 10

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter9: Quadratic Equations And Functions

Section9.6: Graph Quadratic Functions Using Properties

Problem 9.93TI: Graph f(x)=x2+2x8 by using its properties.

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Question

Figure 10 shows a constraint g(x, y) = 0 and the level curves of a function f. In each case, determine whether f has a local minimum, a local maximum, or neither at the labeled point.

Vf
Vf
B
g(x, y) = 0
g(x, y) = 0
FIGURE 10

Formula Formula A function f ( x ) is also said to have attained a local minimum 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 a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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