Question

solve d e f

Question 1 The little details of Fermat's theorem, the first derivative test, and the second derivative test are
important. This problem addresses some common misconceptions about some of these details.
(a) Give an example of a function f such that f(3) is a local maximum and f"(3) = 0.
(b) Give an example of a function f such that f"(3) is undefined but f(3) is a local minimum.
(c) Give an example of a function f such that f"(3)
0 but f is concave up for all x.
(d) Give an example of a function f such that f(3) is a local maximum and f'(3) is undefined.
(e) Give an example of a function f such that f'(3) is undefined, but f(3) is neither a local minimum
nor local maximum.
(f) Give an example of a function f that is increasing for all x, but f'(3) = 0.
Expand
Transcribed Image Text

Question 1 The little details of Fermat's theorem, the first derivative test, and the second derivative test are important. This problem addresses some common misconceptions about some of these details. (a) Give an example of a function f such that f(3) is a local maximum and f"(3) = 0. (b) Give an example of a function f such that f"(3) is undefined but f(3) is a local minimum. (c) Give an example of a function f such that f"(3) 0 but f is concave up for all x. (d) Give an example of a function f such that f(3) is a local maximum and f'(3) is undefined. (e) Give an example of a function f such that f'(3) is undefined, but f(3) is neither a local minimum nor local maximum. (f) Give an example of a function f that is increasing for all x, but f'(3) = 0.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Applications of Derivative

Functions

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Consider the following reaction:If a container were to have 10 molecules of O2 and 10 molecules of N...

A: Click to see the answer

Q: Calculate the approximate molecular weight of a protein composed of 587 amino acid residues in a sin...

A: Proteins are nitrogenous compounds and are macrobiomolecules. They are formed of various amino acids...

Q: Problem 1: Baseball bounces A baseball player throws a baseball to a catcher. The ball bounces once ...

A: Newton's first law states that an object in a state of rest or a state of motion will continue to re...

Q: Figure P5.27 shows the horizontal forces acting on a sailboat moving north at constant velocity, see...

A: Click to see the answer

Q: An ellipse or hyperbola uses the general form Ax? + Cy + Dx + Ey + F = 0. Solving for 5 unknowns (A,...

A: Given: Vertical ellipse or hyperbola x2+Cy2+Dx+Ey+F=0 and the points -1.366, 0, 0, 2.241, 1, -12 and...

Q: Braverman Company has two manufacturing departments-Finishing and Fabrication. The predetermined ove...

A: Total Material=Finishing+Fabrication=$410+$60=$470

Q: Consider the chemical reaction below: Zn + 2 HCI ZnCl2 + H2 where AHrn= -249270J Select the statemen...

A: The balanced reaction taking place is given as, => Zn + 2 HCl -------> ZnCl2 + H2             ...

Q: Based on the graph below, which of the following values for the correlation coefficient is most like...

A: Correlation Coefficient: Correlation coefficient is used to measures the strength of association or ...

Q: Wage and tax statement data on employer FICA tax Ehrlich Co. began business on January 2, 20Y8. Sala...

A: Ans 1) Employee  Gross Earnings       G Federal Income tax witheld Social security tax withel...

Q: The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitaliz...

A: Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials...

Q: Leslie Sporting Goods is a locally owned store that specializes in printing team jerseys. The majori...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: A second-stage smog alert has been called in a certain area of Los Angeles County in which there are...

A: Given, Total number of industrial firms = 50 The selected firms for inspection = 10           To fin...

Q: Transactions; financial statementsBev’s Dry Cleaners is owned and operated by Beverly Zahn. A buildi...

A: The financial statements of the business include balance sheet and income statement of the business.

Q: A uniform rectangular plate of length B = 39 cm and height A = 19 cm has a rectangular corner cut ou...

A: Click to see the answer

Q: Suppose the government wants to reduce the total pollution emitted by three local firms. Currently, ...

A: Externalities refer to the part when the effect of manufacturing or consumption of products and serv...

Q: at is the horizontal distance from the base of t

A: Given: From the observation deck of a skyscraper, Isabella measures a 67o angle of depression to a s...

Q: The table below illustrates the market's demand and supply for a latte. Price[$] Quantity demanded Q...

A: Supply curve increased by 50%

Q: A new company president is said to have caused the company "to do a 180." Before the new president, ...

A: A new company president is said to have caused the company "to do a 180." Before the new president, ...

Q: use Java. In the file RandomNumbers.java, write a class called RandomNumbers that has three integer ...

A:   Answer :

Q: Point P is on line segment OQ. Given OQ = 4x + 2, PQ = 4x 10, and OP = 3x 3, determine the numerical...

A: Click to see the answer

Q: First Mover Advantage   Read the overview below and complete the activities that follow.   When ...

A: First mover strategy: It is a strategy or approach that sometimes is being used by businesses in ord...

Q: Finally, place a new point anywhere on the screen, but not on the perpendicular bisector. Label the ...

A: We will find what we notice abouth the lengths of AF and BF and where we must locate our point F so ...

Q: Aldi is a no-frills grocery chain. It sells grocery staples right out of crates and boxes with empha...

A: upper hand or cost competitive is a bunch of exceptional highlights of an organization and its item ...

Q: A speed boat bought for $13,000 depreciates at 10% per annum compounded continuously. What is its va...

A: Click to see the answer

Q: Convert 16.3 L/cm to units of milliliters per meter. Show the unit analysis by dragging the conversi...

A: Given :- 16.3 L/cm  To convert :- 16.3 L/cm to mL/m 

Q: A thin, circular plate of radius B, uniform surface charge density ?, and total charge Q, is centere...

A: According to Gauss law, the flux linking through a closed loop is given as: ϕ=q∈0 Here, ∈0 is permit...

Q: Shipping A freight company has shipping orders for two products. The first product has a unit volume...

A: Click to see the answer

Q: Organize the physical properties of two identical pieces of foil formed into different shapes. One p...

A: Given here two identical pies of foil formed into different shapes one foil : crumple tightly into a...

Q: The colored lines in the figure represent paths taken by different people walking around in a city. ...

A: Click to see the answer

Q: 1.14 Assume a program requires the execution of 50 x 106 FP instructions, 110 x 106 INT instructions...

A: "AS PER OUR POLICY “Since you have posted a question with multiple sub-parts, we will solve the firs...

Q: Nuthatch Corporation began its operations on September 1 of the current year. Budgeted sales for the...

A: Cash collections refer to the amount of cash collected from the customers on sales and from the debt...

Q: When a proton slows from 0.8c up to 0.6c, it’s kinetic energy decreases by what factor?   Select one...

A: Click to see the answer

Q: When the government makes sure that gas pumps accurately measure the amount of gas they provide, it ...

A: When government intervenes in the market, it tries to resolve the issue of externality, asymmetric i...

Q: Write a program that removes all non-alpha characters from the given input. Ex: If the input is: -...

A: Please find the answer below :

Q: The table shows the number of days on the market for the 36 recent home sales in the city of Sonando...

A: Given data : 112 , 47 , 35 , 153 , 79 , 157 , 11 , 69 , 51 , 147 , 4 , 33 , 78 , 5 , 131 , 113 , 56 ...

Q: Exponential Demand Functions A general exponential demand function has the formq = Ae− bp(A and b no...

A: Click to see the answer

Q: Plant cells are typically 90% water inside, what percentage of the cell contains dissolved solutes? ...

A: The cell is a structural and functional unit of living organisms. Several cells joined together to f...

Q: RS = 3x 16, ST – 4x – 8, RT = 60 Equation: RT 60 RS ST

A: Given that RS = 3x - 16 , ST = 4x - 8 , RT = 60  . We have to find x , RS and ST 

Q: In the circuit shown in the figure the batteries have negligible internal resistance and the meters ...

A: Click to see the answer

Q: A rightward shift of the investment demand curve would be caused by a(an) a. increase in the expecte...

A: Macroeconomics is a part of economics that deals with production, decision and allocation concerning...

Q: Determine the moment of inertia about the axis of the object shown in the figure. Enter your answer ...

A: Click to see the answer

Q: Which statement is true regarding dissociation and dissolution? A. Dissociation can occur without d...

A: Click to see the answer

Q: Quadrialteral GEOM is dilated by a scale factor of 2 centered at (0, 0) to create quadrilateral G'E'...

A: Click to see the answer

Q: List at least ten products that already exist, which you use, that are constantlybeing modified to t...

A: (1) Vehicles (2) Mobile phones (3) Concrete mixers (4) Missiles and fighter jets (5) Water purificat...

Q: During wind erosion, the smallest particles of sediment, composed mostly of silt and clay, are most ...

A:               Wind erosion is a natural process, in which the surface materials were eroded and tran...

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is related to its pressure p (in ...

A: Click to see the answer

Q: 2. Terephthalic acid is a chemical used to make polyesters, including disposable water bottles. It h...

A: Answer 2: chemical formula is  C₈H₆O₄ . Option D) C₈H₆O₄ is correct  

Q: Perpetual inventory using weighted averageBeginning inventory, purchases, and sales for WCS12 are as...

A:     Units Balance Units Cost per unit Total cost oct1 Inventory 320       13 Less:Sale  180  140...

Q: A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. P...

A: Shipping costs are described as the costs associated with the movement of a commodity or a cargo fro...

Q: Determine the total number of nonbonding electrons that should be added to each of these molecules. ...

A: When a chemical bond is formed, some electrons present in their Valence shell participate in chemica...