Question: Show that the equation x3 - 15x + c = 0 has at most one root in the interval [-2, 2].

Show that the equation x3 - 15x + c = 0 has at most one root in the interval [-2, 2].

Step by Step Solution

★★★★★

3.36 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let fx x 3 15x c for x in 2 2 If f has two real roots a and bin 2 2 with a b then fa fb 0 Since ... 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

Document Format (1 attachment)

Word file Icon

786-C-D-E (577).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Show that the equation x3 15x + c = 0 has at most one root in the interval [ 2, 2].

Q:

Show that the equation x3 + 4x3 - 7x + 14 = 0 has at least one real solution.

Q:

Show that the equation 2x 1 sin x = 0 has exactly one real root.

Q:

36. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x) # 1 for all real numbers x, then f has at most one fixed point.17-18 Show that the equation has exactly one...

Q:

On your own paper, answer the following questions using the Intermediate and/or Mean Value Theorems. Show your work neatly and be sure to verify the "if"s of each theorem before using them. A) Show...

Q:

Please explain #19, 20 17. Let f(x) = (x - 3)-2. Show that there is no value of c in (1, 4) such that f(4) - f(1) = f'(c)(4 - 1). Why does this not contradict the Mean Value Theorem? 18. Let f(x) = 2...

Q:

Show that the equation x 3 - 15x + c = 0 has at most one solution in the interval [-2, 2].

Q:

Show that the equation x 3 15x + c = 0 has at most one solution in the interval [2, 2].

Q:

SECTION 4.2 THE MEAN VALUE THEOREM - I 4.2 THE MEAN VALUE THEOREM A Click here for answers. S Click here for solutions. 1-4 - Verify that the function satisfies the three hypotheses of 9. f(x) = 1/x;...

Q:

Show that the equation x3 - 14x + c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x3. -Select- Now f'(r)= 14x + c for x in [-2, 2]. If f has two real solutions a and b in [-2, 2],...

Q:

Taxpayer purchased a personal residence on December 29, 2018 for $266,000. The fair market value of the residence was $280,000 when it was damaged by a flood on June 10, 2019 that resulted from not...

Q:

Question: Woolard Inc. has taxable income in 2014 of $150,000 before any depreciation deductions (Section 179, bonus, or MACRS) and acquired the following assets during the year: (Do not round...

Q:

The payroll register contains all of the following except: a . Hours Worked b . W - 4 Form c . Cumulative Earnings d . Federal Income Tax

Q:

31. Work on a project is ongoing when the proiect m.rnager overhears two workers arguing over what a set I::._ of instructions means. 111e project manager investigates ~mi discovers that the...

Q:

Use the result of Example 3 to evaluate f e**2 dx. *3

Q:

Let f(x) = 0 if is any rational number and f(x) = 1 if is any irrational number. Show that f is not integrable on [0, 1]

Q:

Evaluate the integral. a. b. c. 0 (x - 2x) dx

Q:

When inputting an answer, round your answer to the nearest 2 decimal places. If you need to use a calculated number for further calculations, DO NOT round until after all calculations have been...

Q:

Some recent financial statements for Smolira Golf, Inc., follow. SMOLIRA GOLF, INC. Balance Sheets as of December 31, 2013 and 2014 2013 2014 2013 2014 Assets Liabilities and Owners Equity Current...

Q:

\ table [ [ , Returns ] , [ Year , x , Y , ] , [ 1 , 1 9 % , 1 5 % , ] , [ 2 , 2 2 , 3 4 , ] , [ 3 , 8 , 1 4 , ] , [ 4 , - 1 5 , - 2 0 , ] , [ 5 , 1 0 , 2 4 , ] ] Using the returns shown above,...