Below is the function f(x). 6- 4- 3- -7 -6 -5 -4 -3 -2 -1 4 -3 -4- -6 Over which interval of x values is f' > 0? O (4, 0) O [4, 0) O(- 00, 4) O(- 00, 4] O(- 00, 00] Over which interval of a values is f' < 0? O (4, 0) O [4, o0) O(- 00, 4) O(- 00, 4]| O(- 00, 0] Over the interval ( – 00, 0), this function is concave up (f'' > 0) concave down (f''< 0)

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: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

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: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: Let f(x)=(x-2)(x2+4x-7). Find all the points on this curve where the tangent line is horizontal.

A: The given function is f(x)=(x-2)(x2+4x-7). Since, the slope if the horizontal tangent line is zero.…

Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x&gt;5 We have to find the value…

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: S) Is the function given by 2-4x-5 f(x)= x-5 x+1,x25 .continuous at x = 5? Why or why not?

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Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x&lt;5x+1            ,  x≥5

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

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Q: (3) Show that the function is discontinuous on the specified interval. Vx2 - 64 if x < -8 if -8 <x <…

A: Note: According our answering guidelines we have to answer only one question (if there are multiple…

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

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Q: For what value of the constant k is the function f continuous on (-∞, 0)? 5x2 – kx + 7 if x 7 k =

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Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

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Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

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Q: For −10≤x≤14the function f is defined by f(x)=x^3(x+3)^4 On which two intervals is the function…

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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: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 5) cos (3x). What is the x-coordinate…

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Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

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

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

A: Given:  1. 2.

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

A: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

Q: Suppose that the function y=f(x) is increasing on the interval (-1,5). Over what interval is the…

A: The x-5 is offsetting the input of x. The beginning of the function increase is at x-5=-1 and the…

Q: Suppose the second derivative of f(x) is given by f"(x) = 20x°(x + 5)5(x² + 49). Determine the…

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Q: Suppose the second derivative of a function f is f" (z) 0 (-∞, 1) U (1, 3) U (5,00) ○ (3,5) O (1,3)…

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Q: The derivative of the function f is defined by f'(x) = x? – 5x + 5 cos (3x? – 3x). If ƒ(-2) = –4,…

A: Given: f'x = gx = x2-5x+5cos3x2-3xf-2 = 4------------------------------Aim: To find absolute maximum…

Q: 4 Determine the set of x-values where f(x) 12z is continuous, using interval notation. (-x,5) u (…

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Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: We are given that the derivative of f is f′(x)=3x^2−12x−15 and that f(1)=81.   local maximum?…

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

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Q: Is the function continuous from X = -5 to x = 0? This function is made up of four (4) linear…

A: 1. True, the function is continous from x=-5 to x=0 as there is no break in the       graph between…

Q: 2- By using mumerical approximation ,the value of the derivative (f'(x)) in the table is true f(x)…

A: To find the derivative.

Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

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Q: х — 1 - 2. For f(X) calculate f-'(8) = ? %3D х — 3 -

A: Given : f(x) = (x - 1)/(x - 3), we want to find the function f-1 that takes the value y as an input…

Q: Find an approximation that is accurate to three decimal places to the zero of f (x) = x³ -3x- 1 in…

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.