Suppose f is differentiable on an interval l and f (x) > 0 for all numbers in

Question:

Suppose f is differentiable on an interval l and f ‘(x) > 0 for all numbers in except for a single number c. Prove that f is increasing on the entire interval l.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Jun 30, 2010 01:57 AM

See More Questions

Suppose f is differentiable on R. Let F(x) = f(ex) and G(x) = ef(x). Find expressions for? (a) F (x) and (b) G (x)
Suppose f is differentiable on R. Let F(x) = f(ex) and G(x) = ef(x). Find expressions for (a) F'(x) (b) G'(x).
Suppose f is differentiable on an interval I and f'(x) > 0 for all numbers in except for a single number c. Prove that f is increasing on the entire interval I.
The author explores the dangerous world of undercover police work. Having read this chapter, do you believe this type of police work has the capability of corrupting police officers? If so why, and...
George Company uses the FIFO perpetual inventory method. Information regarding the only inventory item, widgets for the month of April follows: Beginning inventory: 100 units, $10 each April 10:...
Use the U.S. Temperatures data file on the text CD. a. Fit a trend line, and interpret the slope. b. Predict the annual mean U.S. temperature for the year (i) 2010 and (ii) 3000. c. In which...
Show that if $\mathbf{X}^{\prime} \mathbf{X}$ is in correlation form, $\boldsymbol{\Lambda}$ is the diagonal matrix of eigenvalues of $\mathbf{X}^{\prime} \mathbf{X}$, and $\mathbf{T}$ is the...
The shareholders of the Pickwick Paper Company need to elect five directors. There are 200,000 shares outstanding. How many shares do you need to own to ensure that you can elect at least one...
Consider the DFA in Figure. 1. State the 5-tuple description of the DFA. 2. Write the transition table for the DFA. 3. Derive the regular expression defining the language L(M) of the machine. 6 a b
SlowRider Inc. had a rudimentary business intelligence (BI) system. Analysts at SlowRider Inc. pulled data from three different ERP systems, loaded the data into Excel spreadsheets, and e-mailed...
For what values of the numbers and does the function f(x) = axebx2 have the maximum value f(2) = 1?
Assume that all of the functions are twice differentiable and the second derivatives are never 0. 66. (a) If f and g are concave upward on I, show that f + g is con- cave upward on I. (b) If f is...
Sketch an appropriate figure, unless the figure is given. Find the angle of view of the camera lens (see Fig. 4.67), given the measurements shown in the figure. Film diagonal = 42.5 mm 375 mm Fig....
Compare and contrast a labor-based forward rate agreement (interest rate forward) to a euro dollar future. Discuss their respective dates, trading venue, settlement, and convexity.
Do you understand the significant uncertainties, or soft spots, inherent in the organization's strategies for achieving its business objectives and performance goals?
If the company engages in significant trading activities or uses derivatives in a significant way, is the financial and risk management strategy clear?
Can a business-to-business marketer be innovative in the way a brand is built? What are requirements for ingredient brandings, and what are current examples? What industries are more inclined to use...
What is risk and to what extent can it be diversified away when making investment decisions? Explain why the standard deviation may be useful in measuring risk. What are share warrants and what are...
Using an example, how would you explain the logic behind accruals?
The Place-Plus real estate development firm in Problem 24 is dissatisfied with the economists estimate of the probabilities of future interest rate movement, so it is considering having a financial...
If determine whether lim x4 f(x) exists. f(x) = x-4 if x > 4 8- 2x if x < 4
Find the sum of the series.
Find the sum of the series. 3" 5" n! -0
Find the sum of the series. (In 2)? 1 - In 2 + 2! (In 2) + . 3!
a) Give examples of low, medium and high strain rate test types. [4 marks] b) A plot of log (stress) against log (strain rate) provides a straight line relationship. Based on this, provide an...
3- Let the density of the pyramid material be p = 2000 kg/m. Determine the average normal stress at a cross section located at x measured from the apex. Express the stress as a function of x. Assume...
You are designing a wing with no aerodynamic twist based on the airfoil camber given by: N C 3.1 (H-H) = 0.1 The wing will have an aspect ratio of 10, a taper ratio of 0.8, and a constant geometric...

Suppose f is differentiable on an interval l and f (x) > 0 for all numbers in

Question:

Step by Step Answer:

Suppose that f is differentiable on an in...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions