Find a function that is defined for all real numbers and has f'(x) that exists for all real numbers but has f''(x) that doesn't exist for at least one real number

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

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Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

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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 y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

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: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: f(x) = (6x² - 2x+1)^

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what is…

A: answer is in next step. please give a like!!

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given that the derivative of the function f is defined by f'x=x2+2 sin2x-2.   Also f2=7.   Find: The…

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: Find the absolute max and min of the function F(x)= 2sin(x)-cos2(x) on the interval [-π, π]

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Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

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Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

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Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test. Specify whether…

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Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: The derivative of f(x) = ax² will be greater than that of f(x) = ax, for a domain of (0,1), where…

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Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: Find the critical numbers of the function  f(x) = 4x - tan x

A: fx=4x-tanx Differentiating with respect to x, we get f'x=41-sec2x=4-sec2x

Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: Find all critical numbers of f(x)=3x+sin(3x)

A: Given,   f(x)=3x+sin(3x) We have to find all the critical numbers.

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

Q: Show that F(x) = tan2 x and G(x) = sec2 x have the same derivative.What can you conclude about the…

A: Given:Fx=tanx2Gx=sec2x

Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below

Q: IT Uonsəni (a) Use the Second Derivative Test to find the local extreme values of the function f(x)…

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Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.