Q 2. (1) Discuss the continuity of the function f(x) = {x - 3x if x < 2 ( 2x + 4 if x 2 2 on the open interval 0 < x < 2 and on the closed interval 0

Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

Q: Suppose f(x) = x° + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in…

A: Please see the below picture for detailed solution.

Q: ate a continous and differentiable functiin f(x) with the following properties:  f(x) is decreasing…

A: It is given that , f(x) is decreasing at x=-6, f'-6&lt;0 f(x) has a local minimum at x= -3  and f(x)…

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

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Q: 15. Find the end behavior for f(x) = lx - 2| +3 16. Find the end behavior for f(x) = -x' + 5x - 3 A.…

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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: How would you formaly write out a proof for the following problem: f'(1.5) = -1 if f(x) =|x - [x-1]|…

A: Find the derivative at x=1.5 of the function

Q: 6. Sketch an even continuous function with all of the following features: • Absolute maximum at 6 •…

A: We can solve this using given information As we know the even function is nothing but symmetric…

Q: In the function:  f(x)= (4x^2)/((x^2)+4)  What are the critical numbers of the function?  Where is…

A: Given function

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: Find the absolute maximum and minimum values of f(x) = 2x³ + 3z² + 7z – 5, if any, over the interval…

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Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

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

Q: 3. A theatre has determined that its profit function is given by P(x)=x² +9x-11, where x is the…

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

Q: 3. Find the absolute maximum and absolute minimum values of f(x) = 2x´ - 4ln(x) on the | interval […

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Q: 2. Find the absolute minimum and the absolute maximum of the function f(x) = x - 4r +5 on the…

A: Steps to find the absolute maximum and minimum of a function f(x) on [a,b].  : Find the critical…

Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥…

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Q: #11Determine the conditions on parameter k such that the function f(x) = 2x +4 X2-K² will have…

A: According to bartleby guideliness we can answer only the first  3 subpart of multiple…

Q: 5. Find the absolute maximum value on the interval [0,16] for f(x) = (x² – 16x)5 and state its…

A: Concept: If a function f(x) define on interval [a, b] then it's absolute maximum occure either at…

Q: Determine whether the function f(x)= 2x³-3x²-36x+49 is increasing or decreasing at x=5 and x=3. Also…

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

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Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: In the function:  f(x)= 6/((x^2)-16)  What are the critical numbers of the function?  When is the…

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Q: Find where local min/Max occur. f (x) = x³ – 1.5x? – 36x + 2 O local maximum at x = 2; local minimum…

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Q: 6. Sketch an even continuous function with all of the following features: ✔✔✔✔ • Absolute maximum at…

A: We have to draw graph with given information.  Even function means symmetric about y axis.  Y…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: (3) Find the absolute maximum and minimum values of f(x) = x³ – 3x – 1 on the interval [0,3).

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Q: valuate the global maximum and global minimum of the function g(x) = 8 √( x – 4) defined over the…

A: The given function is gx=8x-4 in the interval 4≤x≤29. First  find the derivative of the function,…

Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: B. Find the intervals of increasing/decreasing of the function f(x)=-- 4x +10x² -7. 4 Also find the…

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Q: 3. Find the intervals of increasing/decreasing of the function -4x' +16x² – 20.Also find the local…

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Q: Given the function g(x) = 6x³ + 27x² 72x, find the first derivative, g'(x). g'(x) = 0 when x = -4,…

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Q: Where is there a local maximum on the graph of the piecewise function f(x) = 2x + 5 if x 8?

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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: Can you help with this problem step by step?

A: Given: -

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 - X 0 3

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Q: (i) Show that the line y = 2x – 2 always intersects the curve y = nx² + 6x -n at two distinct points…

A: To solve the problems

Q: Find the absolute maximum and minimum values of f(x) = (x² + x)i over the interval [-3, 4]. absolute…

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Q: 2. Find the absolute maximum value and the absolute minimum value of the function 3 f (x) : 5 – x2…

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Q: 11. Find the absolute minimum and maximum of f(x) = x³ – 4x2 – 3x + 3 on the interval [0, 4].…

A: Given: fx=x3-4x2-3x+3; x∈0,4 for finding absolute minimum and maximum of given function, we draw…

Q: On the interval 0 < x < 3, the function f (x) = x² – 8x + 16, which one it is  a) is concave down…

A: Given:      y=x2-8x+16 , 0 &lt; x &lt; 3

Q: Can you help with this problem step by step?

A: (a)

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

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Q: 7- (a) If a is a constant and cannot be equal to 0, find the critical points of f(x) = 3a + 6x (b)…

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Q: Investigate the connections between key properties such as increasing/decreasing intervals, local…

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

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

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