Question

Which statements about the local maximums and minimums for the given function are true? Check all that apply.

Over the interval [–1, 1,] the local minimum is –8.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.

Answer 1

Answer:

A, C, D and E are true.

Step-by-step explanation:

According to the options, we have,

A. Over the interval [–1, 1,] the local minimum is –8.

We can see that the minimum point is (0.6,-8).

Thus, the local minimum is -8.

So, this is true.

B. Over the interval [1, 3], the local minimum is 0 .

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8 and not 0.

So, this is false.

C. Over the interval [2, 4], the local minimum is –8.

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8.

So, this is true.

D. Over the interval [3, 5], the local minimum is –8.

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8.

So, this is true.

E. Over the interval [1, 4], the local maximum is 0.  

We can see that the maximum point is (2,0).

Thus, the local maximum is 0

So, this is true.

F. Over the interval [3, 5], the local maximum is 0.

We can see that there is no maximum point as the function tends to infinity.

So, this is false.

Hence, the statements which are true are,

A. Over the interval [–1, 1,] the local minimum is –8.

C. Over the interval [2, 4], the local minimum is –8.

D. Over the interval [3, 5], the local minimum is –8.

E. Over the interval [1, 4], the local maximum is 0.  

Answer 2

The true statements are $\boxed{{\text{A, C, D and E}}}.$

Further explanation:

Given:

The options are as follows,

(a). Over the interval $\left[ { - 1,1} \right]$ the local minimum is $-8$.

(b). Over the interval $\left[ { 1,3} \right]$ the local minimum is $0$.

(c). Over the interval $\left[ { 2,4} \right]$ the local minimum is $-8$.

(d). Over the interval $\left[ { 3,5} \right]$ the local minimum is $-8$.

(e). Over the interval $\left[ { 1,4} \right]$ the local maximum is $0$.

(f). Over the interval $\left[ { 3,5} \right]$ the local maximum is $0$.

Explanation:

In option (a)

The local minimum point of the function over the interval $\left[ { - 1,1} \right]$ is $\left( {0.6, - 8} \right).$

The local minimum value is $-8.$

Option (a) is true.

In option (b)

Over the interval $\left[ { 1,3} \right]$ the local maximum value of the function is $0$.

Option (b) is false.

In option (c)

The local minimum point of the function over the interval $\left[ { 2,4} \right]$ is $\left( {3.4, - 8} \right).$

The local minimum value is $- 8.$

Option (c) is true.

In option (d)

The local minimum point of the function over the interval $\left[ { 3,5} \right]$ is $\left( {3.4, - 8} \right).$

The local minimum value is $-8$

Option (d) is true.

In option (e)

The local maximum point of the function over the interval $\left[ { 1,4} \right]$ is $\left( {2, 0} \right).$

The local maximum value is $0$.

Option (e) is true.

In option (f)

Over the interval $\left[ { 3,5} \right]$ the local maximum value of the function is not $0$.

Option (f) is false.

The true statements are $\boxed{{\text{A, C, D and E}}}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: interval, graphed, function, contains, local maximum, maximum, [-1,0], graphed function, functions, local minimum, minimum, statements, over the interval, intervals, true statements.