The relationship between Cunningham Realty's quarterly profits, P(x), and the amount of money x spent on advertising per quarter is described by the following function where both P(x) and x are measured in thousands of dollars. P(x)= -(1/8)x2+14x+30  (0< or equal to x < or equal to 50)   Use differentials to estimate the increase in profits when advertising expenditure each quarter is increased from $21000 to $23000.

Q: Find the derivative of the function.

A: Given: f(x)=x2+5-3x-2 To find its derivative.

Q: The derivative in question, solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3 Determine the largest and…

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Q: Find the derivative of the function.

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Q: Find the derivative of the function G(x) 1 + 2x3 – x2 + 5.3x + /10.

A: GIVEN:   G(x) = 12x4 + 2x3 - x2 + 5.3x + 10

Q: If f(x) = 2x and g(x) = 3x4 - 1. Find the derivative of the product (f×g)(x). 30x 30x4-2 30x³ - 2…

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Q: Find the derivative of the function.

A: fx=x3-2x+3x-3

Q: Find the derivative of the function. g(x) = √(4 − 3x2 )

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Q: find the derivative of the function g(x)=5x^-3+ 6x^-6

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Q: Find the derivative of the function. f(x) = (2x3 − 5x − 9)2

A: Given:   f(x) = (2x3 − 5x − 9)2

Q: Find the derivative of h(x)= (-2x-3)7/ (4x+2)4 You should leave your answer in factored form.

A: To differentiate the given rational function (quotient) in the required (factored) form

Q: 3x +2x-4 derivative of the function of ƒ(x)= %3D 7x² -9x+2

A: f'(x) = (- 41x² + 68x - 32)/(7x² - 9x + 2)²  The detailed solution is as follows below:

Q: The cost to produce a certain commodity is given by the function C(x) = 50x + 2,000 The…

A: The cost to produce a certain commodity is given by the function C(x)=50x+2000. The corresponding…

Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

A:

Q: Find the first, second, and third derivatives of f(x) = x^4 − 2x^3 + 2x^2 − x + 8.

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Q: Find the derivative of the function. h(x) = (4x3 + 2x + 5)/x

A: Given that h(x)=4x3+2x+5x

Q: Find the third derivative of the function f(x)=2x5-7x4+4x2-8x+11.

A: on doing diffrentiation with respect to x we will get

Q: For k(x)=(x−1)(−x2−2x)(2x−2), find the derivative of k(x) using the product rule. Do not include…

A: Obtain the derivative of the function k(x) as follows.

Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

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Q: Find the derivative of the algebraic function. f(x) = (2x3 + 5x)(x − 3)(x + 2)

A: Given function is f(x) = (2x3 + 5x)(x − 3)(x + 2). Simplify the function.…

Q: Find the derivative of the function. y = 2x² +3 x² +1 X y' =

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Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: Find the first and second derivatives of the function. f(x) = √3x-7     f '(x)=   f ''(x)=

A:

Q: Find the derivative of the function. 4 2x - x2 f(x) = %3D x2 - 6 f'(x) =

A: given,        fx=-x2-2x+4x2-6

Q: Find the derivative of the function. f(x) = (2x − 3)4(x2 + x + 1)5

A: Given function is

Q: Find the derivative of the function. 4 3 g(x) = x +4x - 2x - 5 g'(x) =

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Q: f(x) = (x + 2)(2x² – 3) %3D

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Q: Find the derivative of the function. t(x) = x2 − 8x3  / x

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Q: Q8: Calculating Derivatives from the Definition. f(x) = x2 – 3x - 1 %3D

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Q: Find the second derivative of the function.       f(x) = x2 + 3x−3

A: Given: fx=x2+3x-3

Q: Find the derivative of the function. f(x) = (3x + 2)3(x2 + x)2

A: Differentiation use product formula

Q: The Cost and Revenue functions for the production and sale of x hair dryers is C(x)=5x+2340;…

A: Given: The Cost and Revenue functions for the production and sale of x hair dryers:

Q: Find the value of x for which the derivative is zero. y=x3+4x2-3x-5

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Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: Test f(x) = (x3/3) +2x2-5x+1 for relative extrema, using the second-derivative test where possible.

A: For a given function,f(x), at relative extrema x=a, f'(a)=0.The second derivative test is applied to…

Q: Find the first and second derivatives of the function.  f(x) = (x2 + 4)5

A: Rule used:The derivative rules are shown below.

Q: Find the derivative of the function.

A: The given function is gx=3x2-22x+3-2.

Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: Find the first and second derivatives of the function. g(x) = -4x3 + 11x2 + 6x - 51 g'(x) g"(x)

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Q: Find the derivative of the function. x3 4) y =-1 %3D X- 1

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Q: Find the second derivative of the function. h(x) = 6x−2 + 7x2

A: Given function is hx=6x-2+7x2   Differentiate the function with respect to x.…

Q: 3. Derivative of g(x) = 2x + xª − 7x² +3 b) 12x³+4x³ - 14x +3 c) 12x6 +4x² - 14x²_____d) 12x³+4x³ -…

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Q: find the first and second derivatives of the function f(x) = (x2 + 4)5

A: The given function is f(x)=x2+45.

Q: Find the derivative of the function. f(x) = x3 − 2x + 3x−3

A: Consider the following function: fx=x3-2x+3x-3=x3+x-3 Differentiate fx with respect to x:…

Q: Find the first and second derivatives of the function. f(x) = (x² + 5)5

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Q: Find the first and second derivatives of the function. f(x) = x2/ 1+6x

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Q: Find the derivative of y = (x² + 4)²(2x³ – 1)³

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Q: Find the derivative of the function. g(x) = 2(3 - 8x)

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Q: x² +5x +6 f(x) = x² - 4

A: