3a. Give an example of a function f(x) such that • f(x) < 0 • f'(x)...

Question

Question

3a. Give an example of a function f(x) such that

• f(x) < 0

• f'(x) > 0

• f''(x) < 0

3b. Give an example of a function h(t) such that

• h'(t) > 0 when t < −1 and t > 1

• h'(t) < 0 when −1 < t < 1

• h'(−1) = 0

• h'(1) is undeﬁned

math calculus

Answer 1

Answer #1

229 take flu) Since 20 e en zo <0 fluco e- tNER VnGIR also fln) = en 70 tnGIR fln) -- <0 tnER youn function is flu) Hence =

Answer 2

Similar Homework Help Questions

(1)Give an example of a function f : (0, 1) → R which is continuous, but...

(1)Give an example of a function f : (0, 1) → R which is continuous, but such that there is no continuous function g : [0, 1] → R which agrees with f on (0, 1). (2)Suppose f : A (⊂ Rn) → R. Prove that if f is uniformly continuous then there is a unique continuous function g : B → R which agrees with f on A.(B is closure of A)
Example 8.5.1. Let if 0< x< T if 0 or r? -1 if -т <т < 0. 1 f(x)= 0 _ The fact that f is an odd function (i...

Example 8.5.1. Let if 0< x< T if 0 or r? -1 if -т <т < 0. 1 f(x)= 0 _ The fact that f is an odd function (i.e., f(-x) = -f(x)) means we can avoid doing any integrals for the moment and just appeal to a symmetry argument to conclude T f (x) cos(nar)dx 0 and an f(x)dax = 0 ao -- T 27T -T for all n 1. We can also simplify the integral for bn by...
Question 1. Give an example of a complete metric space (X, d) and a function f...

Question 1. Give an example of a complete metric space (X, d) and a function f :X + X such that d(f(x), f(y)) < d(x, y) for all x, y E X with x + y and yet f does not have a fixed point. a map f:X + X has a fixed point if there is an element a E X such that f(a) = a.

PROBLEM 5.3. The function f: R3 R3 given by a bH (3b-a 3a +c 3b +...

PROBLEM 5.3. The function f: R3 R3 given by a bH (3b-a 3a +c 3b + c) is an isomorphism. What is the inverse f-1: R3 R3?
Give an example of a function f(x, y) that is defined on R2 and has only...

Give an example of a function f(x, y) that is defined on R2 and has only hyperbolas as its level sets. At the moment I have x2 - y2 = k (where k is a constant) as my answer. But I'm not sure if that is correct. It seems to work except when k = 0, which I'll have only two lines (y = x and y = -x) so I'm not too sure what should I do with it....
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B...

(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1} (i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...

Give an example of a continuous function f : R → R that is diffierentiable everywhere except at 0 and 1

Give an example of a continuous function f : R → R that is diffierentiable everywhere except at 0 and 1
1. Give an example of a differentiable function f and a point xo in the domain...

1. Give an example of a differentiable function f and a point xo in the domain of f such that f(xo) # Poo(xo), where Poo is the Taylor series of f centered at x = 1. (To be perfectly precise, f(x0) + P(xo) means that lim En(xo) = 0, where En(xo) is the usual error function evaluated at xo.) n- 00 extex 2. The function cosh(x) = = - is called 2 the hyperbolic cosine and has many applications in...
3. Let f be a continuous function on [a, b] with f(a)0< f(b). (a) The proof of Theorem 7-1 showed that there is a smallest x in [a, bl with f(x)0. If there is more than one x in [a, b] with...

3. Let f be a continuous function on [a, b] with f(a)0< f(b). (a) The proof of Theorem 7-1 showed that there is a smallest x in [a, bl with f(x)0. If there is more than one x in [a, b] with f(x)0, is there necessarily a second smallest? Show that there is a largest x in [a, b] with f(x) -0. (Try to give an easy proof by considering a new function closely related to f.) b) The proof...

Give an example of a function f: Σ* x N -> Z , where Σ =...

Give an example of a function f: Σ* x N -> Z , where Σ = {a,b} and where N represents the non-negative integers and Z represents the integers.