Question: Suppose that f C[a, b] is differentiable on (a, b). If f (a) = f(b), then there exists x (a, b) where f(x)

Suppose that f ∈ C[a, b] is differentiable on (a, b). If f (a) = f(b), then there exists x ∈ (a, b) where fʹ(x) 0.

Step by Step Solution

★★★★★

3.39 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By the Weierstrass theorem Theorem 22 has a maximum and a m... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

914-M-N-A-O (809).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

(a) Suppose that f is differentiable on R and has two roots. Show that has at least one root. (b) Suppose f is twice differentiable on R and has three roots. Show that has at least one real root. (c)...

Q:

Suppose that f,g : [a, b] R. Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones. a) If f = g2 and / is...

Q:

Suppose that f,g : [a,b] R. Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones. a) If f and g are increasing on...

Q:

Suppose that f C[a, b] is differentiable on the open interval (a, b). Then there exists some x (a, b) such that f(b) - f(a) = f[x](b - a)

Q:

Let f C[a, b], and let p be in the open interval (a, b). a. Suppose f (p) 0. Show that a > 0 exists with f (x) 0, for all x in [p , p + ], with [p , p + ] a subset of [a, b]. b. Suppose f (p) =...

Q:

solve all on paper please 7. Find a cubic polynomial whose graph has horizontal tangents at(-2,5)and (2,3 8. Prove that - (of (x))=of' (x) using the definition of the derivative. 9. Suppose that f...

Q:

Let f C[a, b] be a function whose derivative exists on (a, b). Suppose f is to be evaluated at x0 in (a, b), but instead of computing the actual value f (x0), the approximate value, (x0), is the...

Q:

Problem 2 (4 points each) In this problem. we will look at some properties of the Riemann integral of the absolute value of a function. (a) Suppose f E 9? 2?,[a b]. Show that |f| 6 3mm] 15]. and that...

Q:

1. Suppose that f : [a, b] R is continuous and differentiable on (a, b), and that for x, y (a, b) with x

Q:

Math 104A Homework #3 Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made....

Q:

A parallel plate capacitor has a charge of 0.020C on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. (a) What is the capacitance for this...

Q:

45 Example 3.3 A double-slit interference pattern is produced on a screen, as shown in Fig. a. The light is monochromatic at a wavelength of 600 nm. A strip of transparent plastic with index of...

Q:

The Excel file Stock Data contains monthly return data for four ( 4 ) stocks. a . Use these returns and the Matrix of Excess Returns to compute the Variance - Covariance Matrix for these four ( 4 )...

Q:

5. Records from an honors statistics class, Experimental Design for Engineers, indicated that each professor had adopted one of three different teaching methods: (A) use of a textbook as the main...

Q:

(a) Find the slope of the tangent to the curve y = 2/(x + 3) at the point where x = a. (b) Find the slopes of the tangent lines at the points whose x-coordinates are (i) , (ii) 0, and (iii) 1.

Q:

(a) Find the slope of the tangent to the parabola y = 1 + x + x2 at the point where x = a. (b) Find the slopes of the tangent lines at the points whose -coordinates are (i), (ii), and (iii) 1. (c)...

Q:

(a) Find the slope of the tangent to the curve y = x3 4x + 1 at the point where x = a. (b) Find equations of the tangent lines at the points (1 2) and (2, 1). (c) Graph the curve and both tangents...

Q:

Suppose 202 animals are classied into 4 categories as follows: Y = (91:92: 293,314) = (125,18,25,34) The corresponding cell probabilities are known to have the structure 91 62 2(1 61) 1 92 61 ( 3 + 3...

Q:

A firm's demand function for product X has the following question: Qx = 1420 -20Px- 10Py + 0.02M + 0.04A where Qx is the quantity purchased, Px is the price of X, Py is the price charged for a...

Q:

Huffman Systems has forecasted sales for its new home alarm systems to be 65,000 units per year at $41.00 per unit. The cost to produce each unit is expected to be about 42% of the sales price. The...