Question: Assume that twice differentiable at c and that has a local maximum at c. Explain why (c) 0.

Assume that ƒ twice differentiable at c and that ƒ has a local maximum at c. Explain why ƒ"(c) ≤ 0.

Step by Step Solution

★★★★★

3.32 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If a function has a local maximum at c it means that c is greater than or equ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus 1st Questions!

Q:

Let I be an open interval, f : I R, and c l. The function f is said to have a local maximum at c if and only if there is a > 0 such that f(c) > f(x) holds for all |x - c| a) If f has a local...

Q:

The function (x) = |x| has an absolute minimum value at x = 0 even though is not differentiable at x = 0. Is this consistent with Theorem 2? Give reasons for your answer. Theorem 2 THEOREM 2-The...

Q:

(a) Sketch the graph of a function that has a local maximum at 2 and is differentiable at 2. (b) Sketch the graph of a function that has a local maximum at 2 and is continuous but not differentiable...

Q:

(2) Let c be a real number in the domain D of a function f. When is the value f (c) an absolute minimum on D? Explain with an example. (3) Let c be a real number in the domain D of a function f. When...

Q:

Please solve the following (2) Let c be a real number in the domain D of a function f. When is the value f(c) an absolute minimum on D? Explain with an example. (3) Let c be a real number in the...

Q:

MAT-225 Calculus module 6 discussion AT-225-J1508 22EW1 Calc I: Single-Variable Calc / Module Six / 6-1 Module Six Discussion: Finding a Function to Match a Shape odule Six Discussion: Finding a...

Q:

a. Suppose a nonconstant even function f has a local minimum at c. Does f have a local maximum or minimum at -c? Explain. (An even function satisfies f(-x) = f(x).) b. Suppose a nonconstant odd...

Q:

Please can you show this using the maxima software, I need this to in this software. Please explain the process and what to type into the software. Thanks Question 7 7 10 marks You should be able to...

Q:

Ap calculus student handout about Concavity, inflection points. Please **step by step and use a **number line as needed to answers the questions. if you could answer the questions in papers instead....

Q:

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Q:

Sketch the graph of y = ln cos x + ln sec x on (-/2, /2) but think before you begin.

Q:

Last year the Chester company increased their equity. In 2022 their equity was $49,360. Last year (2023) it increased to $53,734. calculate What are causes of change in equity?

Q:

what section in the statement of cash flows is for reporting the receipt of cash from dividends?

Q:

AninstructorgivesacoursegradeofBtostudentswhohavetotalscoreonexamsandhome- worksbetween800and900,wherethemaximumpossibleis1000.Ifthetotalscoreshave...

Q:

For the following exercises, test the equation for symmetry. r = 3 3cos

Q:

Given a vector with initial point (4, 2) and terminal point (3, 3), find an equivalent vector whose initial point is (0, 0). Write the vector in component form a, b.

Q:

For the following exercises, find the absolute value of the given complex number. 5 + 3i

Q:

[The following information applies to the questions displayed below.] National League Gear has two classes of stock authorized: 6%, $20 par preferred, and $5 par value common. The following...

Q:

Use the following information for the Exercises 1819 below. (Algo) [The following information applies to the questions displayed below] Following are transactions of Danica Company. Decenber 13...

Q:

Summary Payroll Data In the following summary of data for a payroll period, some amounts have been intentionally omitted: a. Calculate the amounts omitted in lines (1), (3), (8), and (12). (1) (3)...