1. Given that b and c are some nonzero constants, consider the following function: y = f(x) = x + bæ³ + c (a) Find all the extreme points. (b) Find the inflection points of this function:

Q: -. For the function f, f '(x) =x² -1 and f(4) = -1. What is the approximation of f(3.9) found by…

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Q: For what value of x does the function f(x) = x - 9x - 120x + 6 have a local minimum? O A. 4 OB. 10…

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Q: 2. Let f(x) = 2e# – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: PArt A: tangent line at x=1   The derivate of the tangent line at x=1, Find the derivative of the…

Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

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Q: 2 3/2 (1² + 3 + 1)*/² from y = 1 to y

A: Solution

Q: Suppose f is a function where the line tangent to it at x = 3 is given by y = 5x + 2. Find the…

A: Given information: y=5x+2,  Find the value of f(3) and f'(3)

Q: Given that the graph of f(x) passes through the point (9, 6), and that the slope of tangent line to…

A: First calculate f(x) then use (9,6) to find the constant in f(x). Then find f(5).

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: For æ = 4 the function f(x) = x? + bx +c has the minimum value of -9. Fine

A: The given function is f(x)=x2+bx+c has a minimum value = -9 at x = 4.

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: 2. Consider the functions f (x) 1 = - and g(x) = x² – 4 a) Let h(x) = (f ° g)(x). What is h(x)? b)…

A: Given query is to find the composite function and it's domain.

Q: 10.Sketch graph of the following multivariable functions a. z = +1 b. + c. z² = x² ++1 y2

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Q: Given the graph of the derivative f'(x) shown below, which one of the following statements regarding…

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Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

A: minimum cost

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: Determine the values of constants a and b so that f(x) = ax^2 + bx has an absolute maximum at the…

A: Given that  f(x) = ax2 + bx has an absolute maximum at the point (1,2).

Q: ind the critical points of the function f(x, y) = x² + y² + 10x – 9y + 3. List your answers as point…

A: In this question, concept of critical points is applied. Critical Points The critical points of a…

Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: Find k such that the line is tangent to the graph of the function.

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)

Q: Find the critical points of the following function. f(x) = 5x? + 3x +2

A: Given,          The function is fx=5x2+3x+2.

Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: The slope of the tangent line to the graph of the function y=3V-4at (16,8) is 16.00 4. -1.00 O-0.50…

A: Now,

Q: Find the absolute extrema of the function on the closed interval.

A: Solution Given Find the derivative of the functionf'(x)=xx2+1To find the criticle Number derivative…

Q: Consider the following equation below f(x)=4x^3+12x^2-96x+6 a.) Finally intervals on which f is…

A: Given:fx=4x3+12x2-96x+6To find:→Intervals on which fx is increasing→Local minimum and maximum values…

Q: Find k such that the line is tangent to the graph of the function. Function Line f(x) = kv x y = 4x…

A: The function is fx=kx and the equation of line is y=4x+4. Equate both the functions: kx=4x+4k=4x+4x…

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: For function f (x, y) x2+1 Let us consider the level curve f(x, y) = 2. Does the point (1, 2) belong…

A: f(x,y) = y2/(x2+1)  Also,  f(x,y) = 2  We have (x,y) = (1,2)

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: 6. Find k such that the line is tangent to the graph of the function f(x) = k/x and y = 2x + 18.

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Q: A manufacturing company produces two models of an HDTV per week, x units of model A and y units of…

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Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: Given x2 if x 2 f(x) – f(2) a) Determine the left and right limit of the function b) For what…

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Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: find the critical points in the domains of the following functions. y = ( x^2 - 1 ) / (x^2 + 2x -…

A: It is given that the function is y=x2-1x2+2x-3. Obtain the domain of the function as follows:…

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: 4. a) Find the value of x where the function f(x) = (x – 4)3 is not differentiable.

A: According to power rule of differentiation , .

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

A:

Q: Select the graph of a function which has exactly one critical point, at x = 3, and exactly one…

A: We can use the concept of graphical analysis in order to solve the given problem.

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3