On what interval is the function f (x) = increasing? x* + 1 (a) [-2,2] (b) [-2, 1] (c) [-1,2] (d) [-1,1] (e) (– ∞, 1]

Q: 10.6 Find the example of a function f(x) which is continuous at every point of the interval (0, 1),…

A: f(x)=∣x−0.1∣+∣x−0.2∣+   ...........+∣x−0.99 l This is the function which is continuous at every…

Q: What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the…

A:

Q: 7. Let f be a function that has first derivative f /(x) = +2 and second derivative f"(x) = 2-2++2.…

A:

Q: 8. A limit exists if both the right-hand and left-hand limits are equal. 9. The acceleration…

A: Given :   Limit rule, acceleration, quotient rule

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: Xs-1 Let f(x) = {[x+1]-[1-x). -1<x<1 x21 1x|x- where [] denotes the greatest integer function, then…

A: Introduction :

Q: The function f(x) is everywhere continuous and differentiable. Prove that if the function f(x) has…

A: Given that f(x) is continuous and differentiable everywhere and f(x) has two real roots.

Q: The value (x, f(x)) of the maximum or minimum limit of the function 8 + f(x) = x3 - 6x2 + 4x and for…

A: Please see the attachment

Q: 1). Sketch a continuous function f on the interval [-6, 6] that has the following properties:…

A: Note:- As per our guidelines, we can answer the first problem as exactly one is not mentioned.…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

A:

Q: The function In x f (x) = x2 is Select one: increasing on the interval (-o, -) and decreasing on (5,…

A: fx=lnxx2 The domain of given function is 0, ∞. Differentiating with respect to x, we get…

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: # 22 A right circular cone of radius 6m and height 10m is initially filled with water. An empty…

A: We know volume of water in cylinder = volume of cone - volume of water remaining in cone

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

Q: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

Q: The function f has a continuous second derivative, and it satisfies f(-6) = -1, f'(-6) = 0 and…

A: Maxima minima problem....

Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

A:

Q: 3. f(x) = Vx - 5 is continuous on the interval [5, 0) %3D

A:

Q: Sketch

A:

Q: The limit represents the derivative of some function f at some number a. State such an f and a. 16 +…

A: This question is about differentiation expressed as limit of a function

Q: A function, f (x), has derivatives: f'(x) = x² (x – 3) f"(x) = 3x(x – 2) Which of the following…

A: Given data is : A function, fx, has derivativef'x=x2x-3f''x=3xx-2

Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

A:

Q: Find the value of “c” guaranteed by the MVT theorem over the interval [-8,-6] for the function: F(x)…

A: Given function is : Fx=2x3+9x2-60x        -8,-6 To find the value of c.

Q: 5. Find the absolute minimum and absolute maximum values of f(x)= 2cosx +sin2x on the interval 2 N

A: Consider the given function,To find the absolute minimum and maximum values of the given function,…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x&gt;0

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 3x…

A:

Q: 3. Find the absolute maximum and the absolute minimum of f(x) = x-2 tanx on the interval [0,4].

A:

Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: Given, f(x) = 2cox - x              x ∈ [ 0 , 2π] f'(x) = 2 (-sinx) - 1 = -2sinx -1…

Q: The function f(x) = 3 x4-4 x3-12 x2 +1, is decreasing on the interval OA (-00,-2)U(0,2) OB…

A:

Q: 2x is an increasing function for x>0. 2+x Show that y = In (1+x)-

A:

Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

A:

Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

Q: III. Show that the function is continuous on the specified interval. 11. f (x) = V3x – 5; [3,9]

A:

Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

A:

Q: Find all the intervals at which the given function is continuous. 1. f(x) = x - 3x - 10 2. g(x) =…

A: Disclaimer: Since you have posted multiple questions, we will answering the first the questions for…

Q: A periodic function, f(x) with period 4x is defined as 2n. - 2n sx< -A -RSX<0 f(x) = -X . Osx<* 2n,…

A:

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: Given fx=x4-x2 on -2, 2

Q: 1. For the function f(x) = 2x3 - 3x2-36x restricted to the interval [-4,4], %3D (a) Find the…

A:

Q: On the interval x∈(1,2), the curve y=x^3−6x^2+9x+1 is. decreasing and concave down horizontal…

A: Option A is correct..

Q: The function f is continuous for all real numbers and the graph of its derivative function f' is…

A: Given The graph of the derivative of a continuous  f

Q: f f (x) has a local maximum, but no absolute maximum, in the interval [-5,5], then f (x) cannot be…

A:

Q: Prove that f(x) = x-¹/2 is: (i) not sectionally continuous in every finite interval in the range x ≥…

A:

Q: f(x)=12+4x-X ', [o,s]

A: We will use derivative test to find the maxima and minima.

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=x-2tan-1x,  -3, 3 Differentiating with respect to x, we get f'x=1-2·11+x2=1+x2-21+x2=x2-11+x2 a).…

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.