a) Show that there is one value of x for which f(x) and g(x) both have the

Question:

a) Show that there is one value of x for which f(x) and g(x) both have the same stationary value.

b) On the same axes sketch the graphs of f(x) and g(x).

f(x) = 3x² + 2x + 5

g(x) = x³ − 4x² − 3x + 6

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

Step by Step Answer:

Related Book For book-img-for-question

Complete Pure Mathematics 1 For Cambridge International AS & A Level

ISBN: 9780198427438

2nd Edition

Authors: Jean Linsky, Brian Western, James Nicholson

See More Books

Question Posted: Apr 14, 2023 11:22 AM

See More Questions

a. The function f is such that f(x) = 2x 2 - 8x + 5. i. Show that f(x) = 2(x + 1) 2 + b, where a and b are to be found. iii. Hence, or otherwise write down a suitable domain for f so that f -1...
A childs pogo stick (Fig P8.56) stores energy in a spring with a force constant of 2.50 0 104 N/m. At position A (xA = 0.100 m), the spring compression is a maximum and the child is momentarily at...
The function f is such that f(x) = 3x 7 for x . The function g is such that a. Find the value of x for which fg(x) = 5. b. Find f 1 (x) and g 1 (x). c. Show that the equation f 1 (x) = g 1 (x) has...
Suppose that the Medicare rate of hospital reimbursement is reduced. Explain why the costs may not be shifted to other patients in the short run.
Listed here are the total costs associated with the 2015 production of 15,000 Blu-ray Discs (BDs) manufactured by Maxwell. The BDs sell for $18 each. Required 1. Classify each cost and its amount as...
If the joint probability distribution of X and Y is given by f(x, y) = c(x 2 + y 2 ) for x = - 1, 0, 1, 3; y = - 1, 2, 3 find the value of c.
Genetic Diversity and Distance from Africa It is hypothesized that humans originated in East Africa, and migrated from there. We compute a measure of genetic diversity for different populations, and...
You are designing an adder for the blindingly fast 2-bit RePentium Processor. The adder is built from two full adders such that the carry out of the first adder is the carry in to the second adder,...
if V 3 = 1 0 s i n 1 0 0 t and V 4 = 9 s i n 1 0 0 0 t what is the current through the load resistor R 9 at t = 1 9 8 9 . 8 9 5 ? Resistor R 9 is a 1 1 6 watt carbon resistor, does it catch on fire...
On December 31, 2023, RCA Companys Allowance for Doubtful Accounts had an unadjusted debit balance of $7,800. The accountant for RCA has prepared a schedule of the December 31, 2023, accounts...
If show that dy X d.x (5 - 3.x)
A tank in the shape of a right circular cylinder with no top has a surface area of 3m. What height and base radius will maximise the volume of the cylinder?
Under what condition would the stated annual rate equal the effective annual rate (EAR) for a given deposit? How do these rates relate to the annual percentage rate (APR) and annual percentage yield...
Suppose the capacitor in Figure 26.9 has a plate separation distance $d$ and the plates carry charges $+q$ and $-q$ when the capacitor is connected to a battery that maintains a potential...
An open belt drive transmits a power of $5 \mathrm{~kW}$. The linear velocity of the belt is $8 \mathrm{~m} / \mathrm{sec}$. The angle of the lap on the smaller pulley is $165^{\circ}$. The...
A team of automotive engineers want to compare the lifetimes of two brands of tire. They obtain samples of seven tires of each brand. On each of seven cars, they mount one tire of each brand on each...
The article "Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings" (M. Rathhore, A. Chowdhury, and S. Ghosh, Journal of Earthquake Engineering, 2011: 99-123)...
The article "Predicting Depressed Patients with Suicidal Ideation from ECG Recordings" (A. Khandoker, V. Luthra, et al., Med Biol Eng Comput, 2017: 793-805) reports a study in which systolic blood...
Suppose a firm has 20 shares of equity and a 10-year zero-coupon convertible bond with a maturity value of $200, convertible into 8 shares. What is the value of the debt, the share price, and the...
An environmentalist wants to determine if the median amount of potassium (mg/L) in rainwater in Lincoln County, Nebraska, is different from that in the rainwater in Clarendon County, South Carolina....
Do more educated (EDUC) Americans watch less television (TVHOURS)? a. To answer this question calculate a statistic that measures the strength of the linear relationship. b. Calculate the average...
We would expect that people with more education would postpone having children. To examine the relationship between years of education (EDUC) and the age at which ones first child is born (AGEKDBRN),...
How does age (AGE) affect respondents television viewing (TVHOURS)? Conduct a statistical analysis to determine whether the two variables are related and the average marginal increase in television...
Evaluate lim -3x+8 x+4x-4 by graphing.
CONSOLIDATED STATEMENT OF CASH FLOWSfor the year ended 3 1 st December 2 0 2 2 The financial statements are prepared and presented in ???? ???? $ , the functional cuThe notes on pages 7 7 to 1 2 7...
Let p(x) = 6x35x2-2x+1. It is easy to check that p(1) = 0, i.e., 1 is a zero of p. p has two more real zeros. The smaller is x = Hint: Use synthetic division to divide p by x-1, and find the zeros of...

a) Show that there is one value of x for which f(x) and g(x) both have the

Question:

Step by Step Answer:

ANSWER a To find the stationary values of fx and gx we need to find ...View the full answer

Complete Pure Mathematics 1 For Cambridge International AS & A Level

Students also viewed these Mathematics questions