How do I show that F(x) are antidervatives of f(x)?

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: Find f-1 if f (z) = iz + 1.

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Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Differentiate f (x) = vx from first principles. %3D

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

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

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Q: Show analytically that the function f is not differentiable at x = x² x1

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Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: (a) Find the critical numbers of the function f(x) = x6(x – 4)2. (b) What does the Second Derivative…

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Q: 16. Differentiate. f(x) = et %D ex+x

A: differentiating both sides with respect to x and solve the question. see 2nd step.

Q: NOW IT'S YOUR TURN ! Find the critical points of the following functions : 1) f ( x ) = -3 x3 + x 3)…

A: f(x)=-3x13+xfirst differentiate both sides with respect to xf'(x)=-3×13x13-1+1f'(x)=-x-23+1for…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: 22. (a) Find the critical numbers of f(x) = x*(x – 1)°. (b) What does the Second Derivative Test…

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Q: Find all antiderivatives of function:  f (x) = -4x

A: An antiderivative of a function f(x) is the indefinite integral ∫f(x)dx. Denote this antiderivative…

Q: The function f(x) = 2x – 45x + 300x – 5 has two critical numbers. The smaller one is x : %3D and the…

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Q: Please show steps.

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Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

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Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Show two ways to differentiate ƒ(x) =

A: The function f(x)=1x10. We have to differentiate this function.

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: The critical points for the 4 function f(x) = x + – is:

A: Given,          The function is fx=x+4x .

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

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Q: Find the most general anti-derivative of f(x) = 9/x +1+ co x. %3D 9/x- sin x + C 6xVx + x +sin x 6xV…

A: Here I am attaching image so that you understand each and every step.

Q: 8(x) = X -x3 + 2x x4

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Q: Determine the critical numbers of the functions. 1 Ex5 +x +3 1 f(x) :

A: Given query is to find the critical points of the function.

Q: EXAMPLE 2 Find af/ay as a function if f(x, y) = y sin xy.

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Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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