Suppose the function f(x) has a domain of all real numbers except  x = −8 . The first derivative of f(x) is shown below. f '(x) = −5(x − 4)/(x + 8)5 Find the intervals where f(x) is increasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)         Find the intervals where f(x) is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)         Find the x-coordinates of all relative extrema on the graph of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Relative Maxima:              Relative Minima:

Q: On the interval –5 < x < 6, for how many values does f (x)(graphed below) have a derivative equal to…

A: Given:

Q: If f(1) = 3, f'(1) = 4, g(2) = 2, and g'(2) = 8, find F'(1). F'(1) = ... NOTE: This problem is a bit…

A: NOTE: Refresh your page if you can't see any equations. . here we have

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

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

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Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

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Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

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Q: If f'(x) = 3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the local…

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

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Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: -what is the second derivative of i (-1) when i(x) =x^2f(x) -What is the derivative of g(3) when…

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Q: Find the derivative of the given function from the first principle ax2+bx+c

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Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

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

Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: if f(x) = x²√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 5) cos (3x). What is the x-coordinate…

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Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: Find the derivative of the function. y = (x + 1)²(x² + 1) ~ 3 ...... - 2(x + 1)(2x² – 3x – 1) OA.…

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Q: f. y=In(x8+1)

A: We will solve the problem

Q: The first derivative of the given function is y = In(1 – 2x)³(2x + 1)? 10x+1 2x+2 1-4x2 1-4x2 20x+2…

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Q: Consider the function g(x) =2x³ - 6x+3. The critical values for this function are and since these…

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Q: F(x)=In(52x+n • (x+2) ) %3D

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Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

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Q: Find the first derivative of with respect to x using the increment method y=3x^2-7x+12

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Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 +…

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Q: 1. Find the derivative of the following f) y = (2x − 1) ( x³ − x) + √x[2(x³ − x) + (2x − 1)(3x² −…

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Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

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Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

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Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

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Q: 15) Determine the 3rd derivative of the function f(x) = 2\x-x³ [T:2]

A: topic - derivatives

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does…

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What is the first derivative of p(x)=6e^−8x

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Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

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Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…