Aх3+ Bх + 2 , x< 2 Find the values of A & B given that the derivative of f (x) = is everywhere continuous. Bx2 - A „x>2

Q: Use the first derivative to find the local max and min points.  The first derivative is  y’ = -(…

A: Solution:- It is given that  dydx=-(x2+1)(x2-1)2 for critical point  put dydx=0

Q: Let f(x) = 1/(x-5). Find the derivative f' of f. Find an equation of the tangent line to the curve…

A: This questions is related to differentiation,  We will solve it using given information.

Q: CABANATUAN CITY Find the derivative of each function using implicit differentiation. 10. 3y +7x =x2…

A: 10. 3y4+7x=x2+y-311. 2x3y-3y3x+x2y2-2=012. 1x3y3+4y2x=-xy2

Q: a(1+x²) Find the derivative 1-x

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Q: Find the derivative of the function using the definition of derivative. f(x) = ax + n f'(x) = State…

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Q: the Fundamental Theorem of Calculus to find the derivative of the function. Simplify answer 5x g(x)…

A: Topic:- calculus

Q: The derivative of a function is f'(x) x(x + 2)(x - 4). Find the value of x at each point %3D where…

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Q: Find the derivative of f(x): z²+2 . Enclose numerators and denominators in parentheses. For example,…

A: Finding f'(x)

Q: Find the derivative of the function using the definition of derivative. g(x) = the square root of 8…

A: Given,g(x) = 8-x → 1Definition of derivativeg'(x) = limh → o g(x+h) - g(x)h → 2

Q: 3. lim(5 1) x-0 Q2/ Find the derivative of the function f (x) v4 -x by definition !3!

A: When limit is of the form 00or ∞∞ then L Hospital's rule is used . In this rule, take derivative of…

Q: Find the derivative of the function using the definition of derivative. g(x) = v2 - x 1 g'(x) = 2(2…

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Q: A function f(x) has derivative f'(x)= 3x²+ 18x. The graph of f has an x- intercept at x = -1. Find…

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Q: A graph of y=f(x) is shown. In the same coordinate system, sketch a graph of the derivative function…

A: Note: If f(x) is decreasing, then the graph of f'(x) will be below the x-axis. If f(x) is…

Q: 25310+5 25802.20 Evaluate the derivative of the given function at the given point. SHOW ALL WORK.…

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Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

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Q: f(x) = -2x + 4x – 4 Use the limit definition of the derivative to calculate the derivative of f:…

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Q: Ax³ + Bx+2 Find the values of A & B given that the derivative of f (x) =- , x2

A: Derivative of f is continuous everywhere but let's use continuity of f'(x) at x=2 to find A and B .

Q: Find the derivative of the function using the definitionof derivative. State the domain of the…

A: we have to find the derivative of the function f(x)=1.5x2-x+3.7 we have to write the domain of the…

Q: Find the derivative of the function using the definition of derivative. F(x) = x + Vx + 4 1 1+ f'(x)…

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Q: Find the derivative of the function using the definition of derivative. f(x) = x° - 5x + 9 f'(x) =…

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Q: Using first principles (by definition), prove that the derivative of a constant is 0.

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Give an example of a function that is continuous on −∞ < x < ∞, but has NO DERIVATIVE at x = 3.

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Q: 28. F(v) V v+2

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Q: he local maximum and minimum values of the function f(x)=-x-(25/x). using the Second Derivative

A: Given function is fx=−x−25x To find the local maximum and local minimum of the function using the…

Q: Complete detailed solution. What is the derivative of 1 1(x) = (2+²+ -x)(-+1+√x²) x+1

A: To determine the derivative of fx=12x-2-x-1+x4x+1

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given

Q: f(x) = -2x + 8x + 4 Use the limit definition of the derivative to calculate the derivative of f:…

A: f'(x) = -6x2 +8 f"(x) = -12x

Q: xerci if x < 0. (a) For which values of a is f continuous at zero? (b) For which values of a is f…

A: fa(x) = xa if x &gt;00 if x≤0(a) fa(0) = 0 ,  limx→0-fa(x) =0so fa(x) is continuous at 0 if…

Q: Ах3+ Вх + 2 , x2

A: Solved below

Q: A. Using the definition of derivative, find the derivative of the follow function. 1) f(x) = ! 2)…

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Q: 2х+5 9. Find the derivative of the function (x) = Simplify your answer. Show your 2х-3

A: 9. fx=2x+52x-3f'x=22x-3-22x+52x-32=-162x-32f'x=-162x-3210.gx=cos25xg' x=2cos5x-sin5x5g'…

Q: f(x) = -2x + 2x – 4, Use the limit definition of the derivative to calculate the derivative of f:…

A: The function f(x)=-2x3+2x-4. We have to find the limit definition of the derivative to calculate the…

Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: 80. The function f has first derivative given by f'(x) = x* – 6x² – 8x – 3. On what intervals is the…

A: Derivative of the function f(x) is f'(x)=x4-6x2-8x-3

Q: The derivative of a function f(x) , is given by f(x) = (x-2)²cx-5) . For which values of x is f(x)…

A: Given: f'x=x-22x-5 We know that any given functiony=fx is increasing if f'x&gt;0 and decreasing if…

Q: 3. If f and g are the functions whose graphs are shown below, let u(z) = f(g(x)), v(x) g(f(r)) and…

A: Given:-                 u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if…

Q: A 1. Determine algebraically the values of x for which the derivative equals zero. a) f'(x)= 21 + 7x

A: To find the value of of x where derivative equal to zero, we first make the derivative equal to zero…

Q: 6) Find the derivative of y = (3x + 7)2x %3D

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Q: Ах° + Bх + 2 , x32 Find the values of A & B given that the derivative of ƒ (x) =• is everywhere…

A: Givenf(x)=Ax3+Bx+2  , x≤2Bx2-A  , x&gt;2And here derivative of f(x) is continuous everywhere.

Q: Togaritnmic difterenti ation f(X) = (4x3+1) (x? +5)3 to find derivative f'(x) = (20 Use %3D

A: f(x)=(4x3+1)(x2+5)3

Q: x2-3 b) By use derivative sketch the function f(x) x-2

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Q: Using the First Derivative Test, what are the local extrema for the function g(x) - + 9x- 28x + 1?…

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Q: 3.2 The Derivative as a Function ) Usc the Definition, f'=f(xth)- fcx), to find | ん the derivative…

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Q: A. Using chain rule find the derivative of the following functions. 1) f(x) = (x³ + 3x²) 200 2) f(x)…

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Q: Ax³+ Bx + 2 ,x2

A: Given :- f(x) =    Ax3 +Bx+2          , x&lt;=2                Bx2 -A                   , x&gt;2  To…

Q: A function f(x) has derivative f'(x) = 3x²+ 18x. The graph of f has intercept at x = -1. Find f(x).…

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Q: (a) Use Definition 5.2.1(Differentiability). to produce the proper formula for the derivative of…

A: The definition for the differentiability of a function fx at point c is given by f'c=limx→cfx-fcx-c.…

Q: Module 4: Participation Activity #2 p>Find the second derivative of f (x) = a4e" . f" (x) =

A: Given function is Differentiating with respect to x using product rule of differentiation, we get…