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Use the graphing tool to find the local minimum and the local maximum for the given function.

Over the interval [-3, -1], the local minimum is

A) -3
B) -2
C) -1
D) 0

Over the interval [-1, 0], the local maximum is

A) -1
B) 0
C) 1.5
D) 4.39

Over the interval [0, 3], the local minimum is

A) -40
B) -32
C) -18
D) 0

Use the graphing tool to find the local minimum and the local maximum for the given function Over the interval 3 1 the local minimum is A 3 B 2 C 1 D 0 Over the class=

Respuesta :

muradzaini

Answer: 1.D 2.D 3.B

Step-by-step explanation:

Local minimum and maximum corresponds to the minimum and maximum value at y-axis in the graph.

Applying this principle for the given intervals we can see that:

for Interval [-3,-1] min value is 0

for Interval [-1,0] max value is 4.39

for interval [0,3] min value is -32

xero099
  • Over the interval [-3, 1], the local minimum is 0, since [tex]f(-2) < f(x),\forall \,x \neq -2, -3 \le x \le -1[/tex]. Right choice: D.

  • Over the interval [-1, 0], the local maximum is 4.39, since [tex]f(-0.8) > f(x),\forall \,x \neq -0.8, -1 \le x \le 0[/tex]. Right choice: D.

  • Over the interval [0, 3], the local minimum is -32, since [tex]f(2) < f(x), \forall \,x \ne 2 , 0 \le x\le 3[/tex]. Right choice: B.

Given a function that is continuous for an interval [tex][a, b][/tex], [tex]a \neq b[/tex], then there is a local minimum and local maximum if and only if:

  • Local minimum:

[tex]f(c) < f(x), \forall \,x \neq c[/tex], [tex]a \leq c \leq b[/tex] (1)

  • Local maximum:

[tex]f(d) > f(x), \forall x \neq d, a \le d \le b[/tex] (2)

Based on these facts, we proceed to solve each question:

  • Over the interval [-3, 1], the local minimum is 0, since [tex]f(-2) < f(x),\forall \,x \neq -2, -3 \le x \le -1[/tex]. Right choice: D.

  • Over the interval [-1, 0], the local maximum is 4.39, since [tex]f(-0.8) > f(x),\forall \,x \neq -0.8, -1 \le x \le 0[/tex]. Right choice: D.

  • Over the interval [0, 3], the local minimum is -32, since [tex]f(2) < f(x), \forall \,x \ne 2 , 0 \le x\le 3[/tex]. Right choice: B.

We kindly invite to check this question on maxima and minima: https://brainly.com/question/2292974

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