Assume that exists and (x) > 0 for all x. Show that (x) cannot be negative
Question:
Assume that ƒ" exists and ƒ"(x) > 0 for all x. Show that ƒ(x) cannot be negative for all x. Show that ƒ'(b) ≠ 0 for some b and use the result of Exercise 62 in Section 4.4.
Data From Exercise 62 From Section 4.4
Prove that if ƒ" exists and ƒ"(x) > 0 for all x, then the graph of ƒ“ sits above” its tangent lines.
Transcribed Image Text:
(a) For any c, set G(x) = f(x) = f'(c)(x - c) - f(c). It is sufficient to prove that G(x) > 0 for all c. Explain why with a sketch. (b) Show that G(c) = G'(c) = 0 and G"(x) > 0 for all x. Conclude that G'(x) < 0 for x < c and G'(x) > 0 for x > c. Then deduce, using the MVT, that G(x) > G(c) for x = c.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (5 reviews)
Data From Exercise 62 From Section 44 Let fx be a ...View the full answer
Answered By
Ashish Bhalla
I have 12 years work experience as Professor for Accounting, Finance and Business related subjects also working as Online Tutor from last 8 years with highly decentralized organizations. I had obtained a B.Com, M.Com, MBA (Finance & Marketing). My research interest areas are Banking Problem & Investment Management. I am highly articulate and effective communicator with excellent team-building and interpersonal skills; work well with individuals at all levels.
4.80+
17+ Reviews
46+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Assume that " exists and let c be a point of inflection of . (a) Use the method of Exercise 62 to prove that the tangent line at x = c crosses the graph (Figure 21). Show that G(x) changes sign at x...
-
Use the result of Exercise 27 and the fact that /2 cos x dx = 1. (From Exercise 25 in Section 5.1), together with the properties of integrals, to evaluate /2 (2 cos x 5x) dx
-
Which is not a difference between a limited liability company and a limited liability partnership? a. An LLC, unlike an LLP or LLLP, can exist with only one owner. b. All members of an LLC have...
-
Davenport Construction Associates compares actual results with a flexible budget. The standard direct labor rates used in the flexible budget are established each year at the time the annual plan is...
-
Do cell phones distract drivers and cause accidents? Worried that this is happening, many states recently have passed legislation to reduce distracted driving. Fourteen states now have laws making...
-
If a PV array has a maximum power output of \(10 \mathrm{~W}\) under an insolation level of \(600 \mathrm{~W} / \mathrm{m}^{2}\), what must the insolation be to achieve a power output of \(17...
-
Sycamore Company uses a certain part in its manufacturing process that it buys from an outside supplier for $29 per part plus another $4 for shipping and other purchasing-related costs. The company...
-
When a field goal kicker kicks a football as hard as he can at 45 to the horizontal, the ball just clears the 3-m-high crossbar of the goalposts 45.7 m away. (a) What is the maximum speed the kicker...
-
1. Case Exhibit 2 presents monthly data of units produced and sold, and actual costs incurred, for 24 months. B Create a scatterplot of costs and units. b. From your scatterplot, estimate the...
-
Lets find out what has happened to Microsofts (MSFT) dividend policy since its 2003 announcement to initiate dividends. We can address this issue by relying on the data that are provided to you in...
-
Assume that ' and " exist for all x and let c be a critical point of . Show that (x) cannot make a transition from ++ to + at x = c. Apply the MVT to '(x).
-
1. Sharps Sandwich Shop has two conflicting quality issues speed and freshness. The premade sandwich system enhances speed; however, it has the potential of affecting freshness. What type of system...
-
Concord Company has the following account balances: Sales Revenue $ 2 1 1 , 4 0 0 , Sales Discounts $ 4 , 3 1 0 , Cost of Goods Sold $ 1 3 8 , 6 0 0 , and Inventory $ 4 3 , 9 0 0 . Prepare the...
-
In January, Blossom Company requisitions raw materials for production as follows: Job 1 $ 1 , 1 6 0 , Job 2 $ 1 , 4 0 0 , Job 3 $ 7 8 0 , and general factory use $ 7 0 0 . During January, time...
-
Firm A has a margin of 1 0 % , sales of $ 5 1 0 , 0 0 0 , and ROI of 1 9 % . Calculate the firm's average total assets. Firm B has net income of $ 7 4 , 0 0 0 , asset turnover of 1 . 5 0 , and...
-
Ellie runs a labour hire firm in which she provides suitably qualified staff to businesses involved in the hospitality industry including hotels, motels and restaurants. She has three full-time...
-
How do ethical considerations in external auditing impact the trust and reliability of financial reporting?
-
Many small retailers advertise in their neighborhoods by sending out flyers. People deliver these to homes and are paid according to the number of flyers delivered. Each deliverer is given several...
-
An access route is being constructed across a field (Figure Q8). Apart from a relatively firm strip of ground alongside the field's longer side AB, the ground is generally marshy. The route can...
-
A discrete random variable that counts the number out of two molecules that are in at time 1. Think about one or more molecules independently leaving a cell, each with probability 0.9 in a given...
-
A discrete random variable that counts the number out of two molecules that are in at time 2. Think about one or more molecules independently leaving a cell, each with probability 0.9 in a given...
-
Experiment a. For the data presented in Section 6.6, Exercises 37-40, write the results in terms of a random variable and find the expectation. What fraction of experiments have a result less than...
-
One of the interesting things we can do with nested loops is generate dynamic patterns based on user input. We'll start off by making a simple demonstration of this - a checkerboard pattern. You will...
-
Consider the following CSP. A, B, C and D are variables with their domain of values as given below: A = {1, 2, 3} B = {1,2,3,4) C = {1,2,3} D = {1,2} The constraints are: = AB {(1,1), (2,2), (3,3)}...
-
Rewrite the following partial EBNF grammar in BNF notation. You are allowed to create new non-terminals in order to define the LHS non-terminals properly. You do not need to create rules for the...
Study smarter with the SolutionInn App