Question: Let f be continuous on [0,1], differentiable on (0,1), f' is increasing on (0,1) and f(0) = 0. Show that the function g(x) =

Let f be continuous on [0,1], differentiable on (0,1), f' is increasing on (0,1) and f(0) = 0. Show that the function g(x) = f(x) is increasing on (0,1]. x (3 marks)

Step by Step Solution

★★★★★

3.49 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To show that gx fxx is increasing on 01 prove that gx ... 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!

You will demonstrate your mastery of the following competencies: Evaluate tax laws, regulations, and codes for diverse financial situations Prepare complex income tax returns that adhere to tax laws,...

Let f be continuous on a closed, bounded interval [a, b] and suppose that DRf{x) exists for all x (a, b). a) Show that if f(b) y0} satisfies f(x0) = y0...

This is True or False 1. If a function is itegrable then it must be differentiable. 2. The fact that f is an integrable function implies that there always exists a differentiable function, F(x), such...

Let f be continuous on [a, b], let f(x) > 0 for x [a, b], and let Mn :(ba fn)1/n. Show that lim (Mn) = sup{f(x) : x [a, b]g.

nitrogen - 1 3 undergoing positron emission Express your answer as a nuclear equation.

(c) A inction at, y) is dierentiable at (a, b) if and only if the linear approximation is a good approxi- mation of the function near the point (a, b). In other words, the surface 2 = f(l':, 3;) near...

How would you know that a more capable code couldn't be made? [1 mark] (b) The sign to-upheaval extent SNR of a constant correspondence redirect might be different in different bits of its repeat...

Directions Complete the following 2 FRQ problems They each have 4 parts a d associated with them and each are out of 9 points total 1 Particle A is moving along the x axis Let f be the continuous...

Please help with example problems 1-3. 1. \f2] Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all a? E (a, b). Prove that there 3:55) = + Fla. (Hint: consider...

4. Recall Taylor's Theorem in one variable, which states the following. Taylor's Theorem in one variable. Let / C R be an open interval and let x* E I. Let f : I - R be n + 1 times continuously...

Theorem 1 If lim f x L and lim f x M then L M x p x p IL MI Proof Suppose L M then IL MI 0 Since lim f x L if we take 2 then 38 0 such that x p Ix pl 8 f x LI E Similarly since lim f x M 38 0 such...

(d) A solution of [Ni(HO)]+ is green and paramagnetic (u =2.90 BM), whereas a solution of [Ni(CN)4] is colorless and diamagnetic. Give a qualitative explanation for these observations (2 Marks) (e)...

What is the degree of operating leverage for Company A and Company B? (Round to two decimal places)

Now find the absolute value of z . | z | = | - 0 . 4 1 | =

Use the "OUTLINE" and the "MINDMAP" to design a presentation for training others about race-related stress on black children and provided "Evidence-based" solutions based on the references included....

Sale-leaseback DExample IFRS and ASPE Company A sells a machine to Company B for its fair value of $ 2,000,000 on January 1,2018 Company A immediately leases the machine back for 5 years The useful...

A bakery produces fresh bread daily. Each loaf of bread costs $2.50to make and sellsfor $5.00. Unsold bread at the end of the day must be discarded, leading to a loss. Thebakery estimates the...

Let n N, let a R", let s, r R with s

Show that og x

If k=1 akxk has radius of convergence R and ak 0 for large prove that lim inf|-|

15. Before LTP: In the normal state, what is the effect of glutamate at the AMPA receptors? At the NMDA receptors?

17. After the neuron has gone through LTP: What is now the effect of glutamate at the AMPA receptors? At the NMDA receptors?

1. The left hemisphere of the brain is connected to the right eye in rabbits. In humans, the left hemisphere is connected to the left half of each retina. Explain the reason for this species...