Show that if f(x) ax 3 bx 2 cx d, then Deduce that f(x) 3ax 2 2bx c f(x Ax) ax bx cx d (3ax 2bx c)Ax (3ax b)(Ax) a(Ax)...

fx ax bx cxd fx Ax ax Ax bx Ax cx Ax d ...

Show that if f(x) = ax 3 + bx 2 + cx + d, then Deduce that

Question:

Show that if f(x) = ax³ + bx² + cx + d, then

f(x+Ax) = ax + bx + cx+d+(3ax +2bx+c)Ax + (3ax + b)(Ax) + a(Ax)

Deduce that f’(x) = 3ax² + 2bx + c

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

See More Books

Question Posted: Jan 13, 2024 09:06 AM

See More Questions

Show that if f (x) = ax3 + bx2 + cx + d, then f(k) = r, where r = ak3 + bk2 + ck + d, using long division. In other words, verify the Remainder Theorem for a third-degree polynomial function?
Consider f(x) = Ax3 + Bx2 + Cx + D with A > 0. Show that f has one local maximum and one local minimum if and only if B2 - 3AC > 0.
Data is fitted to a cubic f = ax 3 + bx 2 + cx + d with the slope of the curve given by f' = 3ax 2 + 2bx + c If f 1 = f(x 1 ), f 2 = f(x 2 ), f ' 1 = f'(x 1 ) and f 2 = f(x 2 ), show that fitting the...
How does the winner of a lawsuit enforce the judgment?
A sample of an ideal gas is taken through the cyclic process abca shown in Figure. The scale of the vertical axis is set by p?? = 7 .5 kPa and pb = 2.5 kPa. At point a, T = 200 K. (a) How many moles...
The investments officer for Sillistine Savings is concerned about interest rate risk lowering the value of the institutions bonds. A check of the bond portfolio reveals an average duration of 4.5...
Learned how to find probabilities of discrete events by using the probability rules of Chapter 3. LO8
Suppose that peoples expectations of inflation are subject to random shocks. That is, instead of being merely adaptive, expected inflation in period t, as seen in period t 1, is Et1 t = t1 + t1,...
Saved Help Save & Bannister Co. is thinking about having one of its products manufactured by a subcontractor Currently, the cost of manufacturing 1.000 units follows: Direct material Direct labor...
The displacementtime graph for a vehicle is given by Obtain the formula for the velocitytime graph. s(t)= t-t+1, 3t - 3, 19-t, 0t1 1
Show from first principles that the derivative of Hence confirm the result outlined in blue in Section 2.3.4 and using the calculus method verify the results of this example. Data from Section 2.3.4...
Suppose that each U.S. worker can produce 8 units of food or 2 units of clothing daily. In Fredonia, which has the same number of workers, each worker can produce 7 units of food or 1 unit of...
Exercise 11-5 Profit allocation in a partnership LO3Dallas and Weiss formed a partnership to manage rental properties, by investing $161,000 and $189,000, respectively. During its first year, the...
operation research an introduction by Taha, Hamdy A . 2 0 2 2 . Operations Research - An Introduction. 1 1 th ed . Prentice Hall..kindly explain this
which 2 statements are correct regarding budgets in quickbooks online? a . budgets can be created to track capital expenditures. b . budgets can be set up bsed on the last fiscal year's financial...
Dr. Yong has requested that Senture Houston, an office manager at Pain Free Dental Associates, prepare a single journal entry for December 31, 2022. The bank statement for that day shows $9,500....
This program will not require any IF statements, loops, or custom classes. Instead, it will check inputted data for two kinds of mistakes: Wrong data type (entering text instead of numbers), and math...
Suppose that individuals of type b reduce the per capita type a growth rate by half as much as individuals of type a, and that individuals of type a reduce the per capita type b growth rate by half...
Suppose the concentration of glucose inside a cell is 0.1 mm and the cell is suspended in a glucose solution of 0.01 mm. a. What would be the free energy change involved in transporting 10-o mole of...
Methionine enkephalin is a pentapeptide that is produced by the body to control pain. From the sequence of its amino acid residues, draw a bondline structure of methionine enkephalin. N terminus C...
Draw a bond-line structure of the peptide that corresponds with the following sequence of amino acid residues, and identify the N terminus and C terminus: Trp-Val-Ser-Met-Gly-Glu
Draw the predominant form of Asp-Lys-Phe at physiological pH.
Suppose the S&P 500 currently has a level of 960. One contract of S&P 500 index futures has a size of $250 S&P 500 index. You wish to hedge an $800,000-portfolio that has a beta of 1.2. (A)In order...
Exhibit 4.1 The balance sheet and income statement shown below are for Koski Inc. Note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during...
Haley is 57 years of age. She is planning for future long-term care needs. She knows that yearly nursing home costs in her area are currently $69,000, with prices increased by 5 percent annually....

Show that if f(x) = ax 3 + bx 2 + cx + d, then Deduce that

Question:

f(x+Ax) = ax + bx + cx+d+(3ax +2bx+c)Ax + (3ax + b)(Ax) + a(Ax)

Step by Step Answer:

fx ax bx cxd fx Ax ax Ax bx Ax cx Ax d ...View the full answer

Modern Engineering Mathematics

Students also viewed these Sciences questions