Given the function: f(x)=(x^2-2 where, x<4 and 2x+7 where x >/= 4). State whether the function is continuous at x=4

Q: Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Given f(x)=(1+2x2)(x-x2) By Product rule,…

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: How do I tell if it’s continuous

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Q: g(x) = at x = 2 %3D x+2

A: Definition of continuous function helps to check whether the given function is continuous or not. A…

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Find the absolute extrema of the function on the closed interval. f(x) = 7 – x, - [-4, 4] minimum…

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Q: List the x-values where the function is not continuous: f(x) = -x+ 3 if ex if if 3 – x x < - 3…

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Q: Use derivative rules to compute f'(-1) given f (x) = -4x8-32x - 4.

A: f(x)=-4x8-32x-4Formula: xn'=n xn-1

Q: = x3-122 +2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use the second derivative test todetermine whether f(x)=-2x³+6x2-3 has a localmaximum or…

A: Given,          fx=-2x3+6x2-3

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: Find the number c which will make the function continuous on (-00, 00). x< 2 f(x) = x+ c, x22

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Q: Give an example of a function that is continuous but differentiable at x=2

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Q: Find the local maximum and minimum values of f using the Second Derivative Test. If the Second…

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Q: use th eproduct rule or the quotient rule to find the derivative of f(x)=(x^2+x-8)/x^2-8

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Q: f(x)= (7x¹-5x-2)

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Q: Compute the derivative. f(x) = (2x 4 - 4x- 1) secx

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Q: if cosh(x)=41/40 and x > 0, find the other hyperbolic functions of x

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Q: If   f(x) = 8x2 arctan (9x2),  find f’(x)

A: Explanation of the solution is given below...

Q: Use the second derivative test (is possible) to find the relative extrema of f(x) = 3x^4 - 8x^3 +…

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Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

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Q: Compute for f '(3) using the limit definition of derivative if f(x) - 6x²

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Q: Find the points on the graph of f(x) = 6x – 2x³ where the tangent line is horizontal. (Use symbolic…

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Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: Use Intermediate Value Theorem to show that the equation

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Q: f(x)%3DX4-3x3 + 2x2 - 5x-7 at x = -1

A: Given:     fx=x4-3x3+2x2-5x-7      at  x=-1 1. f(c) must be defined.  The function must exist at an…

Q: Use derivative to identify open intervals on which the function is increasing or decreasing.…

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Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: Explain how the Intermediate Value Theorem (IVT) can be used

A: Intermediate value theorem is stated as follows. Consider an interval I=a,b of real numbers ℝ and a…

Q: Suppose that f(x) = 17ex - exe Find f'(3)= ?

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: At the point x 2, the function -8 2<x<* f(x) = |x-2 -< xs2 is (a) continuous and differentiable (b)…

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Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)

Q: Explain why functions with cusps are not differentiable even though they are continuous.

A: Derivative is a slope, defined by a limit.   In order for a derivative to exist, it needs to be…

Q: Explain Why functions with cusps are not differentiable even though they are continuous.

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Q: Determine whether the function shown is continuous over the interval (-5, 5).

A: We will determine whether the function is continuous over the interval (-5, 5) as following.

Q: Find all relative extrema of the function f(x) = x² - 4x² + 2 by using the Second Derivative Test…

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Q: Give the result of every step in using the 4-Step Rule to find the derivative 14. f(x) = x3- 4x² + x…

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: 3lim %3D f(x+h)-f(x) to find f'(x) for f(x) = -4x2+2x+3. = (),f

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

Q: Find f"(x) f(x)= J3x-7

A: Given that, The function f(x) is, f(x) = 3x-7 We have to find the second derivative of the given…

Q: f(x)=√√x at x = 7

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Q: Can the Mean Value Theorem be applied to the function f(x) = 1/x2 on the interval [−2, 1]? Explain

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Q: By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the…

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