15 if a < - 9 Net f(x) = T2 + 9x- 6 if a> – 9 If f(x) is a function which is continuous everywhere, then we must have

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: d) A function with no absolute extrema but with a local minimum of -5 at x = 4 and a local maximum…

A: Follow the procedure given below.

Q: The graph of a continuous function f is shown in the figure above. If g(x) = / f(t) dt, a then g(x)…

A:

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

A:

Q: Suppose a tour guide has a bus that holds a maximum of 86 people. Assume his profit (in dollars) for…

A: Solve the following

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Find the global maximum and minimum for the function on the closed interval. x + 1 f(x) - 1<x< 2 x²…

A: We have to find global maximum and minimum.

Q: There exists a field that is populated with a large amount of sunflowers. The amount given in time t…

A: Consider the given equation, y(t)=10004+t-12πcosπ6t   Find the derivative of the function.…

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

A:

Q: If an odd function f(x) has a local maximum value at X=c which of the following must be true?

A:

Q: True or FalseA 1. A Step-function is continuous at every point in its domain

A: Given: A step - function is continuous at every point in its domain. To write: The given statement…

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

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

A: Maxima minima problem....

Q: 7. Consider the function *+1 if r< 2 f(x) = 3-1 if z 2 2 (a) Show that ƒ has no fixed point.

A:

Q: 10 if x c - everywhere then: С —

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Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

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Q: Q3) if the continuous function is : 4x+1 F(x) -+k at x= h. Find the value of h,k.

A: 3). Given function is:   fx=4x+1x&lt;hx3+kx=hx2+1x&gt;h Solution: A function fx is continuous at x=h…

Q: The total number of local maximum and minimum points of the function whose derivative, for all x, is…

A: 1st derivative of function is f'(X) =x(x-3)^2(x+1)^4 For critical point we must have f'(X)=0 Hence…

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

A:

Q: 19 – x² ; if x 3 continuous or not on the interval [0, 3].

A: Given function: fx=9-x2;if x≤3x-3;if x&gt;3 The objective is to determine if the function is…

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 value of the constant c such that the function f(x)= (x-2)/( (root 4x+1)-3) if x#2, c if…

A: And

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: 2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b)…

A: f(x) = x3 − 27x For critical points, f'(x) = 0 ∴f'(x) = 3x2 - 27 = 0 =&gt;3(x2 - 9) = 0 =&gt; x = ±3…

Q: 1. Give an example of a function f : R –→ R that is continuous and bounded but does not achieve…

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

Q: The function ff has a continuous second derivative, and it satisfies f(1)=2f(1)=2, f′(1)=0f′(1)=0…

A: Given: f(1)=1, f'(1)=0, f'(1) = 2 A critical point of a function occurs when the first derivative…

Q: ind the absolute maximum and absolute minimum value of f(x) = 12 + 4x – x on [0, 5)

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Suppose a function y = f(x) is defined for all values x -1. The derivative of (z²+1)e² ze² f(x) is…

A: Given is a function y=f(x) which is defined for all value except -1.   Also, given f'x=x exx+12,…

Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) f'(x) > 6 for all x. = -2…

A: Given, fx is differentiable everywhere. f-4=-2 f'x≥6, for all x dydx≥6, for all x  dy≥6dx…

Q: Q.4. locate the critical points of the function f(x) = x²(x-1)³ and identify critical points which…

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Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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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: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: 1 - X 0 3

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: x+4 if x2

A:

Q: A continuous function, h(x) has a local maximum at (2, 3). What is h’(2)?

A: We have given that h(x)  is a continuous function and has a local maximum at point (2,3).

Q: The function f(x) = 1+x has a local minimum when a = 0. Select one: O True O False

A:

Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Q: x²-a if x2 is continuous at x-2, then x+3 if x-2 If the function fo)

A:

Q: 2. Give an example of a function f: (0, 00) → K that is continuous and bounded but does not achieve…

A: It is an usual example which derivative not vanish anywhere

Q: x² - 2x-8 if x+ 4 (4) F(x) =, x-4 if f is continuous at x=4, а, if x = 4 then a =.

A: Topic:- limit and continuity

Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…