Determine all of the points of inflection of the function f (x) = x* – 8x² O The points of inflection are (-2, – 48), (0, 0), and (2, – 48). O The points of inflection are(-2, – 48) and (2, – 48). O There are no points of inflection. O The points of inflection are (, 2/3 2/3 -80 and -80 3 3

Q: (2) For the f(x) = -x3 + 3x + 6 determine the coordinates of the turning point(s) and any point(s)…

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Q: The domain of the function 15z + 7 is Z-1 S(z) = f(x) O R-(7} O R-(15} O R-(1} O R-(0} OR

A: f(x) = 15x+7x-1Denominator is x-1;if x=1then Denominator is 0.10 is not defined.

Q: For the function f(x)==-x - 24x+19 3 (i) Determine the turning points and the values of the function…

A: Increasing  and Decreasing Functions: A function f(x) is called increasing on an interval I if given…

Q: (c) Determine the values of x for which the function f (x) = {x+ 2 2x2 x5 is discontinuous. x25

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Q: Locate the absolute extrema of the function f(x)=-2r+ 12x+ 3 on the closed interval [-6, 6].

A:

Q: a) Find 2 x-intercepts of the function f (x) = a² + 6x . The x-intercepts are and (write smaller…

A: a) The x-intercepts of a function is the points where the graph crosses x-axis . The values of y…

Q: Q3: Find the extreme values of the function f(x, y) = xy – 3x2 - y? + 3x - 3y + 8.

A: To find the extreme values of  f(x,y)=xy-3x²-y²+3x-3y+8

Q: Find f. f"(x)  =-2  +12 x -12 x2   , f(0)   = 4 ,f'(0)  =12

A: Given ,f''x=-2+12x-12x2f0=4f'0=12

Q: Q7:- Find the extreme value of the function f(x,y) = 4xy - x - y*. Q8:- Find the extreme value of…

A:

Q: Determine the values of x for which f (x) = 1x − 4 is increasingand for which decreasing

A: fx=1x-4 Differentiating with respect to x, we get f'x=-1x-42    ∵ddx1x=-1x2

Q: f For the functions f(x) = 2-x and g(x) = x + 4x- 32, find f+ g, f-g, fg, and De

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Q: Determine all inflection points. 3 f(x) = 4x° - 12 , xER

A: Find all inflection points  fx =4x3-12 inflection point is point where f''(x) is equal to zero or…

Q: Q6:- Find the extreme value of the function f(x, y) = 3x2 - 2xy + y2 - 8y.

A: First, let us find the partial derivatives of the given function as shown below:…

Q: x2 + x – 2 At which value of x does the function f(x) have a removable x3 – 3x2 + 2x -…

A:

Q: Given the function P(x) = (x – 2)*(æ – 8), find its y-intercept is its x-intercepts are x1 = and x2…

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Q: Find the interval on which f is concave up and Find the interval on which f is concave down. Enter…

A: If F"(x)>0 then F(x) will be concave upIf F"(x)<0 then F(x) will be concave down.

Q: Q2// Sketch the graph of the function defined by the formula 0, xS-1 f(x) ={V1-x2 ,-1<x<1 x21

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Q: (4x + 7 (ii) If f(x)={ 4x -1 18xs2 , determine whether the function f(x) is continuous 2<x<4…

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Q: . Determine the values of a, b, and c such that the function f(x)=x²+ax² +bx+c has a y-intercep of 1…

A: Solving question

Q: (4x+7 (ii) If f(x) = { 14x²-1 Isxs2 2<154 determine whether the function f(x) is continuous…

A: In this question we have to check whether the given function is continuous throughout its domain or…

Q: For the function g(x) 3x*-2x2 + 6, find the intervals where the function is concave up and the…

A: Given, g(x)=3x4-2x2+6

Q: Graph the function f (z) = –4x³ – 2z² +7z – 2. Use the graph to order the function values from least…

A: The given function is: fx=-4x3-2x2+7x-2 Graph of this function is:

Q: Q4: Evaluate the function at the given values f(x) = v20 – x² when x = - 4

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Q: For the function f(x) = x3/3 - x2 - 24x + 19 (i) Determine the turning points and the values of the…

A:

Q: 2. Determine the function f (x) for which f'(x) ==++ 3 1 + 8x3 x-2 x2 and f(1) = 7.

A: =&gt; f(x)= ∫ f'(x)dx

Q: Q2// Sketch the graph of the function defined by the formula 0, xS-1 f(x) ={V1-x2,-1<x<1 x , x21

A: We have to sketch using the function in the suitable intervals.

Q: Find f' (x) using the QUOTIENT RULE if 2 – x2 f(æ) 4+ x² f' (x) = Find f'(2). f'(2) =

A:

Q: 4 Find the domain of f(x) x + 3

A: Given:  fx=4x+3 To Find: Domain of the given function fx

Q: Find the absolute extrema of the function f(x) = x* - 72x + 1296 on the interval [-7,7].

A: To find: The absolute extremum of the given function

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: 4. For the functions f(x) = Vx -3 and g(x) = Vx+2, find and detemine the domain in ease case. a. gf…

A:

Q: Let f(x) = 6 + V2x + 11. Find ƒ ¯'(x). f- (x) = where the domain is [6, ∞)

A: The inverse function of a given function y=f(x) can be obtained by interchanging y and x in the…

Q: Find f(5) and f (x² + 3) for the function f(x) = -x + 2 %3D

A: Given,           f(x) = -x + 2

Q: Find f- (x) for f (x) = 1+ 8x. Enter the exact answer.

A:

Q: Find the interval in which the function given by y = 4x3 - 6x2 – 72x + 30 is decreasing. O A. (-…

A: Given that the function is      y = f(x) = 4x3-6x2-72x+30 Here we have to find the interval in which…

Q: 4) For the functions f(x) = √(x-3 ) and g(x) = √(x+2 ), find and determine the domain in each case:…

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Q: Find all the inflection points of the function. f(x) x3+2x2 + 3 3 %3D

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Q: find the domain of the function  f(x) = 1-2cosx / 1-2sinx

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Q: Determine where the function is concave downward. f(x)= -x^2+8x+8

A: Given, f(x)= -x^2+8x+8 We know that, We can calculate the second derivative to determine the…

Q: (c) Determine the values of x for which the function f(x)= %3D 2x2 - 4 x5 7 x>5 is discontinuous.

A:

Q: Determine whether or not the function is homogenous. x5 f(x,y) = 72=2y² If it is homogenous state…

A: Given that: f(x, y)=x5x2-2y2

Q: What is the point of inflection for the function f(x) = x³ – 3x + 1? O The point of inflection is…

A: Find point where second derivative is zero

Q: Find the domain of the function. f(x) = x2 – 10x – 14 What is the domain of f? O A. (-00,00) O B.…

A: Answer is- Option A is correct

Q: Find all y-intercepts and x-intercepts of the graph of the function. F(x) = 2x^3 + 2x^2 – 18x –…

A: The given function F(x)=2x3+2x2-18x-18

Q: Find the greatest and the least values of the function y = x³ – 3x +3 on the 2 (a). interval [-, ).

A: Solve the following

Q: (c) Using the IV.T., explain why f(x) = x³'+ 2x – 1 has a zero in the interval [0, 1].

A: I have the state the theorem first and by using the statement i have show the root

Q: A blogger earns R(x) = 10x + 0.063x² in revenue, where z is the number of subscribers, and has a…

A: This question is based on Revenue and Profit.

Q: Given the function f (x) = 10 + 5x³ – 3x³, identify the interval(s) where the function is concave…

A: Given:      f(x) = 10 + 5x3 - 3x5

Q: For the function f(x) = x2 /3 minus x2 - 24x + 19 (a) determine the turning points of the values of…

A:

Q: Find the domain of the function. (Enter your answer using interval notation.) k(x) =, Vx+4 x - 2

A: Given function k(x) = x+4x-2TO find : Domain of the function

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.