Math

CalculusQ&A LibraryDetermine whether each of the following statements is true or false, and explain why in a few sentences1. A critical number c is a number in the domain of a function f for which f ′ ( c ) = 0 or f ′ ( c ) does not exist.2. If f ′ ( c ) > 0 on an interval, the function is positive on that interval.3. If c is a critical number, then the function must have a relative maximum or minimum at c 4. If f ′ ( c ) exists, then f ″ ( c ) also exists5. If f ″ ( c ) > 0 on an interval, the function is increasing on that interval.Question

Asked Nov 20, 2019

6 views

**Determine whether each of the following statements is true or false, and explain why in a few sentences**

**1. A critical number c is a number in the domain of a function f for which f ′ ( c ) = 0 or f ′ ( c ) does not exist.**

2. **If f ′ ( c ) > 0 on an interval, the function is positive on that interval.**

**3. If c is a critical number, then the function must have a relative maximum or minimum at c**

**4. If f ′ ( c ) exists, then f ″ ( c ) also exists**

**5. If f ″ ( c ) > 0 on an interval, the function is increasing on that interval.**

Step 1

Since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentioned the subparts you need help with. Please resubmit the question and specify the other subparts you’d like to get answered.

Given:

- A critical number c is a number in the domain of a function f for which f ′ (c) = 0 or f ′ (c) does not exist.
- If f ′ (c) > 0 on an interval, the function is positive on that interval.
- If c is a critical number, then the function must have a relative maximum or minimum at c

Step 2

Solve (1):

A critical number c is the number in the domain of a function f for which f ′ (c) = 0 or f ′ (c) does not exist**.**

It is a true statement because it is the definition which is definition of critical number.

A critical number of a function *f* is a point *x* = *c* in the domain of ‘*f* ‘such that either *f* ′(*c*) = 0 or *f* ′(*c*) does not exist.

Step 3

part (2):

If f ′ (c) > 0 on an interval, the function is positive on that interval.

It is the true statement by the definition of strictly inc...

Find answers to questions asked by student like you

Show more Q&A

Q: Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that...

A: Click to see the answer

Q: The area A of the region S that lies under the graph of the continuous function is the limit of the ...

A: Find the area under the graph f(x).

Q: f(x,y)=x^2+9y^2 What is the direction in which f changes most rapidly at point (1,2)?

A: Click to see the answer

Q: Find determine each infinite geometric series whether it converges or diverges if it converges find ...

A: Given series is

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: Problem 3 Please

A: Given the function

Q: 4.6.29-BE Question Help A commercial cherry grower estimates from past records that if 25 trees are ...

A: Let x be the number of trees more than 25.Then total number of trees becomes,

Q: A rancher has 4,648 feet of fencing available to enclose a rectangular area bordering a river. He wa...

A: Let the figure of the fencing be:

Q: is this question talking about a rectangle within a rectangle?

A: Find the dimensions for the whole poster.