Evaluating functions by using derivatives

Reference no: EM13128581

Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5<or equal x< or equal 1.5. The second derivative of f has the property that f''(x)>0 for -1.5<or equalx<or equal 1.5

Find a positive real number r having the property that there must exist a value c with 0 < c < 0.5 and f''(c) = r. Give reasons for your answer.

x -1.5 -1.0 -0.5 0 0.5 1.0 1.5

f(x) -1 -4 -6 -7 -6 -4 -1

f'(x) -7 -5 -3 0 3 5 7

Reference no: EM13128581

Questions Cloud

Real analysis functions with equal derivatives : Let f be a function given by-Is there a function g: R ---> R such that g'=f? Be careful applying definition of the derivative

How many moles of a monoprotic acid must dissolved : How many moles of a monoprotic acid with a Ka=4.9x10^-6 must be dissolved in 750 ml of H2O to produce a solution with pH=4.50

Income in his federal income tax return : Based on the following, how much should Ben Brenner include in income in his federal income tax return? Jury awarded punitive damages $10000 Kickbacks on ...

Find probability that among wrong answers made by men : People who answered incorrectly, 26 are men. The question was given to an equal number of men and women all with the same IQ. Find the probability that among 120 wrong answers, at least 82 made by men.

Evaluating functions by using derivatives : Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5 0 for -1.5

To an athlete dying young : What essential elements of the Modernism period are found in Alfred Edward Housman's poem "To An Athlete Dying Young"? How does "To An Athlete Dying Young" relate to the Modernism period?

Monthly net operating income or loss : If the president is right, what will be the effect on the company's monthly net operating income or loss? Using the incremental approach in perparing the answer?

Define a solvent for an industrial process : A solvent for an industrial process requires the use of phenol or benzene. Both are about the same in effectiveness for the process, and of course, gloves will be used when handling either solvent

Find linear correlation coefficient temperature and chirps : Find the least-squares regression line to predict chirps per second based on temperature. increase in temperature. Predict the chirps per second if it is 83.3 degrees.

User Account

All Pages