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

Question

02-08-2022
Mathematics

Answered

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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

Sagot :

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yogeshkumar49685 yogeshkumar49685 · Answer 1 · 2022-08-05T09:24:22-04:00

The local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.

Given a graph of a function.

We are required to find:

A)Local minimum over the interval [-3,-1],

B) Local maximum over the interval [-1,0],

C) Local minimum over the interval [0,3].

We know that local maximum is a point after which the value of function starts decreasing and the local minimum is a point after which the value of function starts increasing.

When we see the graph from x=-3 to x=-1 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at x=-2 and y=0, so the value of local minimum will be 0.

When we see the graph from x=-1 to x=0 we can find that the highest point is where the value of f(x) is maximum and after which the graph is decreasing is at y=4.39, so the value of local maximum will be 4.39.

When we see the graph from x=0 to x=3 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at y=-32, so the value of local minimum will be -32.

Hence the local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.

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