Question What is f' (x) when f(x) = In ( )? 5x2+2x+3 Select the correct answer below: f'(x) = 10x+2 5 5x2+2r+3

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Derivative of f(x)=1+ 2x+3xy computed * O explicitly equal to 2+3x implicitly equal to 2+3x+3dy/dx O…

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Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: To find the antiderivative we integrate the given function c=integration constant

Q: (8) Find the derivative of the functions (iv)f(x) = e* arcsin x arcsin 3x (v)h(x) = x' arctan 2.x…

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Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

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Q: Can you help me with this problem step by step?

A: The equation is given by

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

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Q: An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For…

A: Let x be the additional number of trees to be planted to maximize the total yield.

Q: The function f(x)=6x^{2}+2x-1 is the derivative of F(x). It is known that F(0)=-1.5. Determine the…

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Q: 3. U sin g Derivative Product rule 3. (x + 6) (x + 5); 4. 4x² (x – 1)

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Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

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Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

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Q: Find the numerical second derivative value f''(0.5) from the data set using the finite difference…

A: given the function is f(x)=x3+0.4x2+x find the derivative  f'(x)=3x2+0.8x+1 again find the second…

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: The maximum rate of change of the function 1 f(x, y) = at the point (1, -2) happens in direction of…

A: I have find the direction and value of maximum rate of change of given function and say that given…

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)   f ( x…

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Q: 4.) f (x) 3D х2 – 1

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Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

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Q: 3) Find the second derivative of 2x f(x) = for x + 0 3x2+4x Show all steps. Simplify your answer as…

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Q: Find the derivative of f(x)=((e^x)+(x^2))(3sinx+4cosx

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Q: Consider the function f(x)f(x) whose second derivative is f''(x)=4x+3sin(x)f′′(x)=4x+3sin(x). If…

A: Consider the function f(x) It's second derivative is f''(x)=4x+3sin(x)If f(0)=3 and f'(0)=4   We…

Q: 7 Find the derivative of f(x) 4/ + x4 Type your answer without fractional or negative exponents. Use…

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Q: 5. Find the average rate of change of the function f(x)= cos² x from x =- x = ". Use to - exact…

A: Rate of change=f(b)-f(a)b-a Given:  f(x)=cos2x, x=-π6,π4

Q: he value x = ! is a critical number of the function f(x) = x ln(x), which has x) = 1+ ln(x). Use the…

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Q: Find the relative extrema of f(x) = 9 + 30x – 5x? using both first and second derivative tests. f(x)…

A: Derivative one time and equate it to zero to find the critical point. Derivative second to find the…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: find the equation of tangent line of function f(x)=csc(x)-cos(x)1/2 at the point ((2*3.14)/3,…

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Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: y=-sinx . 3π X 2 元 2. 2 N/2

A: Given: y=-sinx

Q: b) Use second derivative test to find absolute maximum and minimum values of f (x, у) 3 Зху — 6х —…

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Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sin x 2x-x-1…

A: We have to solve

Q: using the forward divided difference approximation with a step of 0.5, what is the derivative of…

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Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: A function is given by f(x) = 2x3 – eX. The first derivative of f(x) using forward difference method…

A: Consider the given function. fx=2x3-ex The forward difference method is defined as. f'x≈fx-fx-hh…

Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

Q: Find the most general antiderivative of the function. (Check your answer by differentiation.)

A: We have to find antiderivative of the function and we have to check the answer by differentiation:…

Q: 2. Use the definition of the derivative to find the first and second derivatives of the function. 1…

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Q: What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.

A: Given,  f(x)=−3cos(x)+4sin(x)   We have to find the derivative of fx  at  x = π3

Q: what’s the derivative ? f(x)= ln(x^3 - 7x^2 + 1)

A: topic - derivative of a function

Q: Appy the second derivative test to find the absolute maximum value on (0, 0) for f(x) = 15-4x

A: Given function is, f(x)=15-4x-250x2

Q: Q1. (1) The finite-divided difference approximations of the first derivative of the function f(x)…

A: The order of approximation deals with the Taylor series with a remainder. When the error is…