1. (a) A function f is increasing on (a, b) if. when- ever a < x1 < x2 < b. (b) A function f is decreasing on (a, b) if . when- ever a < x1 < x2 < b. (c) A function f is concave up on (a, b) if f' is on (a, b). (d) If f"(a) exists and f has an inflection point at x = a, then f"(a)

Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

A:

Q: 13. Find the end behavior for f(x) =x- 2 A. x- +0, f(x) - +o x--o, f(x) → - B. x +o, f(x) - +0 x--o,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

A:

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: Suppose that the increasing function ƒ(x) is smooth for x &gt;= 0 and that ƒ(0) = a. Let s(x) denote…

A: Given information:

Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have;  f(x)=x32

Q: Calculate limh→0 f(x+h)-f(x) for f (x) = /2x+3. %3D h f(x+h)- f(x) /2x+3 limh0 h -2(2x+3)…

A:

Q: Compute the derivative of f(x) = x³/2 using the limit definition. Hint: Show that f(x + h) – f(x) _…

A: We  will compute the derivative of given function  by using first principle of derivative

Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

A:

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

Q: (9) F(<) = { —1, if - п <x<0 1, if 0sxп (h) f(x) — f -х, х, -1<x<0 0<x<1 if if

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: 15. If f(x) = x2 - 6x - 9, find f(x) by using the formula/limit definition of derivative.

A: Given: fx=x2-6x-9 we know that derivative for any given functionfx by using limit definition is…

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: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: -7 if x 2. Sketch the graph of the function and use the limit definition of the derivative to show…

A:

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

A:

Q: (b). Find the bound for absolute error at x = 2.9 on the interval [x, x,], where x, = 2.25, x, =…

A: On the interval x0,xn where x0=2.25, x1=2.5, x2=2.75, x3=3 with n=3 along with the function…

Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: 5) Suppose that f is the function implicitly defined by the equation + tan ( In = evi near the point…

A: Given:       x+y4+ Tanin xy = ey   →1    near the point ( 4, 4 ) eTo Determine: f is an increasing…

Q: At what points are the functions continuous x -X- g(x) = X - 3 y " 5, x = 3

A: Given:  1. 2.

Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

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Q: Show that x + is increasing on [1, 0).

A:

Q: Suppose that a one-to-one function f has tangent line y=5x+3 at the point . (1,8)Evaluate (f-1)'8

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Q: marginal value

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Q: 1. Does there exist a differentiable function f that is continuous on the closed interval [1, 4],…

A: Mean Value Theorem (MVT):   If f(x) is continuous on the closed interval [a, b] and differentiable…

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: 1. Let f(x) = 2 %3D Use the limit definition of the derivative to compute f'(-1). X+3

A:

Q: the average revenue is defined as the function ------- R(x)=R(x)/x       (x>0)   Prove that if a…

A: The average revenue is, Rx=Rxx  at x&gt;0. Differentiate Rx=Rxx with respect to x.…

Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: generate a continuous and differentiable function that is decreasing at -6, has a local minimum at…

A: