Question: Let f(x) be a differentiable function on [0,2] with f(0) = 1, f(1) = 0 and f(2) = 5. (a) Show that there exist

Let f(x) be a differentiable function on [0,2] with f(0) = 1,

Let f(x) be a differentiable function on [0,2] with f(0) = 1, f(1) = 0 and f(2) = 5. (a) Show that there exist a a2 (0,2) such that f(a) = a and f(a2) = a. [5 marks] (b) Show that there exists b (0, 2) such that f'(b) = b. [5 marks]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a By the Intermediate Value Theorem since fx is continuous on 02 and f0 1 and f2 5 there exists a ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Diamond Company's total overhead costs at various levels of activity are presented below: Machine hours Total overhead costs March 60,000 $216,800 April 50,000 194,000 May 70,000 239,600 June 80,000...

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Find the values of the parameter p > 0 for which the following series converge. In k

Propose a mechanism for the hydrolysis of N,N-dimethylacetamide (a) Under basic conditions. (b) Under acidic conditions.

=+d Master-budget capacity utilisationthe strengthening share market and the growing popularity of motorcycles have prompted the Marketing Department to issue an estimate for 2014 of 3600 units....

For a binary response variable ????, how are the odds that ???? = 1 computed?

The following account balances were selected from the records of Blake Corporation at December 31, 2009, after all adjusting entries were completed: Common stock (par $20; authorized 100,000 shares,...

The T-accounts for Equipment and the related Accumulated Depreciation-Equipment for Pronghorn Company at the end of 2022 are shown here. Equipment Beg. bal. 80,300 Disposals 21,900 Acquisitions...

How different is the NEO Window Shopping script from the traditional window shopping script? How many different analogous scripts would consumers have to draw on to build their expertise in using the...

XYZ corporation a company that sells everyday products, currently has a stock price of 100, with 1 million shares available for trading. XYZ is thinking about growing internationally as part of its...

Draw the context diagram and level-0 DFD to model the process described below. If you feel the narrative is incomplete, make some reasonable assumptions to complete the story. It is important that...

5.You own a software company which supports audits done by civil and mechnical engineers. The software has orginally been sold to private and municiple organizations which monitor buildings and...

Reville LLP is auditing the Year 1 financial records of Renschler LLC, a publicly traded manufacturing company. Renschler has a December 31 year-end. Reville LLP performed their year-end audit during...

Let f C C, differentiable at the origin, f(0) = 0, and satisfy f(2z) = 2f(z) for all z = C. Prove that there exists c E C such that f(z) = cz for all z = C.

Present two of Kaiser Permanente's competitors and explain whether you believe they are a prospector, defender, analyzer, or reactor. ( Class- Strategic Management)

what are concerns with using a polyalphabetic cipher in 2 0 2 4 ?

According during to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,088 in 2018. Consider the population of "last-minute" filers who mail...

1. Show that the cube C2 = {x R2: - c 2. Suppose for any n = 2, 3, . . . , that the cube Cn-1 conv{(±c, ±c,. . . ±)} Rn-1. Show that n-dimensional cube Cn conv{(±c,...

Why would anti symmetry be an inappropriate assumption for the consumer's preference relation?

Using (2), show that for every x , e-x = 1/ex ex > 0 ex as x and ex 0 as x - This implies that the exponential function maps onto +.

8. Is it reasonable to conclude that Brocas patients have lost their grammar?

1. What is change blindness?

9. Describe the speech comprehension of people with Brocas aphasia and those with Wernickes aphasia