1. If f(x) = 2x – x² and g(x) = |x – 3|, find the value of f(-2) + g(-2)

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: b) Given h(x) = 3x² + 2x and f(x) =- Vx – 2, find (h • f) (x + 2)

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Q: If f'(x) = 2x- x-2, then f has inflection point(s) with x – coordinate(s) equal to

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Q: Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 5 and the range of f(x)…

A: Given: The domain of fx is 1≤x≤5 The range of fx is -3≤y≤6

Q: Which is equal to (x) given that g(x) = 1- 3x and h(x) = V?

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Q: 2. Supposef(x) = 5ax³ – 6x² – b²x – 7, and g(x) = cx* + 10x³ – (d + 1)x² – 4x + e. Find values for…

A: The given polynomials are fx=5ax3-6x2-b2x-7 and gx=cx4+10x3-d+1x2-4x+e. We have to find the value of…

Q: F(X)= x^3-18x^2+81X  inflection points occur at x=

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Q: 5. State the equation of f(x) if D = {xER\x - and the y-intercept is (0, ;) 2x+1 x+1 f(x) : f(x) а.…

A: Equation of the function

Q: If we use the secant method on f(x) = x+x3+3 with X-2 0 and Xn-1 = 1, then Xn is_

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Q: Зах + 3 for x -2

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Q: x²–1 If f(x) and g(x) = Vx – 1, which will yield (f 0 g)(x)? %3D r2

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Q: 2. If f(x) = g(x) × h(x) and f'(x) = -2(x – 7) + 1(-2x – 6) , find a possible equation for f(x)

A: see below the answer and explanation

Q: 1. Solve for the values of x in the function below. f(x)=x3-4x-0.5x2+2

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Q: 2. Given that f(x) = 2x + 2 and g(x)= find fg 2+x2

A: Given:  fx=2x+2gx=-x2+x2 To Find:  fggfg1=?

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: x²-3x-4 if x>-1 x- 4 if x < -1 10.Why is f(x) = %3D x-4 discontinuous at x = -1?

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: b) f(x) = V3 + x² at x = -1

A:

Q: 10.Given f(x)=2x-3 and g(x)= x² + 1, solve f[g(x)]

A: We have to find fgx where functions are given as: fx=2x-3 and gx=x2+1. Here we have to find…

Q: x- 2 if xS-2 2 1. Sketch: f(x) = - 2 2

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Q: If f(x) = x° and g(x) = 0.5f(x), what is the value of g(x) at x = 2? %3D

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Q: The function f(x) = 2x³ – 21x² + 60x – 7 has two critical values. The smaller one equals and the…

A: The given function is f(x)=2x3-21x2+60x-7

Q: From Variation of parameters for the 2 -1 X' X + e 3 -2

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Q: Find the extreme values of the function f(x) = x3 + 9x² + 5 on the interval x E [-1,3]

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Q: (a) f(x) = 2r3(3 – 4x)

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Q: Find the inflection point of the curve f(x)=2x³ – 30x² – 12x+5. O 60 None O -2 O 5

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Q: evaluate h(x) = 2x-1/ 3x+1 at the given value of x h(s-5)= ?

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Q: 2. Let f(x) = 16x 4x and g(x) = 18x + 3. Solve for x when f(x) = g(x)

A: We will solve for x when f(x)=g(x)  in the following step.

Q: Find f'(a) for x2 f(x) = x + 6 at a = 3.

A: Given function :

Q: Find Critical numbers of the given function: x² +5 f(x) = %3D x - 2

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Q: 4. F(x)- F(x)=L x-1 5. Gx)-8-2x 6. h(t)= 2-1

A: For a real valued function f(x) We have to find all points x where f(x) is well defined Those points…

Q: Find the absolute extremum values of f(x) = x² – 3x + 8 over the interval [1, 3].

A: First we find critical value and then use first order derivative test.

Q: f(x) = 27x² + 3x5 - 24x³ + √2x f(x) = + √2x 3 x x5

A: Find the general anti-derivative F(x) + C for the following problem:

Q: s given by: (A(x² – 2x + 2) f(x) = ЗА 3 <x< 4 otherwise ere A is a constant

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 1 For what value of x does the function f(x) = =x³ – 4x attain the absolute maximum - in the…

A: here option (c) is true on doing differentiation we get the  f'(x)=3x^2/3-4 f'(x) =x^2-4 put f'(x)…

Q: If FIX) is an antiderivative of x-2 + x1, then what is the value of F(1) - F(-1)? A) 3 (в) -2 -1

A: Solved below

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

A: Given f(x) = cx2+8x   if x&lt;5x3-cx  if x≥5               we find the constant C is the function f…

Q: 2 Given f(x) = x“ - 2 and g(x) 4x + 1, find a. f g b. g(f(x))

A: We will find f .g and g(f(x)) in the following step.

Q: If f(x) = x² find a ō such that 0 < lx - 21 < & implies 1x² - 41 < F when = 1.

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Q: What is the value of In[f'(2)]if f (x) = e*?

A: Our Aim is to tell the value of ln f'(2) if f(x)=ex-(i)

Q: 16. Let f(x) = x² + 10x + 28 m, find m if the function only has 1 (ONE) x-intercept. -

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Q: 4 If f'(x) = x³ x'-2x +x+2, then f has inflection points at 3. n X=0 X= -0.5 X-1 x-0.6 X-2

A: Point of inflection  Those points where cancavity changes called inflection points

Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: 3. For f(x) = x - 10, find the solution to f(x) = 5.

A: f(x) = x - 10 f(x) = 5

Q: 5 If f(x)=g(x)+3 where 2<xs 5, then [[{(x)+g(x)]dx = 2ſ8(x)+3.

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Q: Find the critical numbers of the function. a. f(x) = x3 + 6x? – 15x b. g(x) = V1- x2

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Q: The derivative of f(x) 4 (22 +17x) is O -4c (2a + 17) O -4r 2(2x + 17) O 4x + 68 O 4x 2(2x + 17) O 4

A: Here, it is given that f(x)=4x(x2+17x) We need to find the derivative of the function f(x).

Q: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

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Q: Find the x-values of the stationary points of the function  f(x) = x^4 + 4x^3 - 4x^2 - 24x

A: Given: f(x)=x4+4x3−4x2−24x

Q: b) f(x) = v3+ x² at x = -1

A: