In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval notation?  What are the x-values of all inflection points?

Q: Find the Derivative f(x) = cosh(In(4x))

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Q: use the limit definition of a derivative to find f'(x) f(x)= sqrtx+5

A: See the details solution in below

Q: What is the Range of f(X) = log X? None of these. (0, ∞) (- ∞, ∞) (3, 0)

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Q: Evaluate the second derivative at this critical number.

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Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: Find f' usip , derivative rues Fの =x°(x -ス) %3D

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Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

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Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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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: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: 13. f(x) = e* In x

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Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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Q: 8. Find the derivative of y = x arctan 2.x --In(1+4x). -- - 4.

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Q: Find the derivative by the limit process. f(x) = 14-x²

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Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

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Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: Find the derivative of the function f(x) = cosh(8x + 1)

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Q: a) f'(-3) where f(x) = 5-3x

A: Derivative using definition

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

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Q: Find an equation of the tangent line to the graph of f ( x ) = 2x2 - 10 over 2x - 2 at the point on…

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Q: Find the derivative f(x)= Inlex+9)

A: To find: the derivative of f(x)

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: Use the limit definition of the derivative of a function to find the derivative of f(x) = 4x at x-5

A: From the given problem:   fx=4x2   From the limit definition of the derivatives:…

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: Use the graph to estimate the open intervals on which the function if increasing or decreasing, Then…

A: Given that: The equation of the function f(x) =1(x+1)2 . Graph:

Q: Use the first derivative test and the second derivative test to determine where each function is…

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Q: Find the derivative off (x) = 9x - 5 at x = 2 and x = 5.

A: Given f (x) = 9x - 5

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: f (x) %3D х3 -Зх2- 2 3x2

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Q: 1. Find the derivative of f(x). 3x3 – 2x2- x- 5 | (a) f(x) =

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Q: f(x) = - sin(2x) on the interval TC

A: f is maximum at x = - π/4 f is minimum at x = π/4   The detailed solution is as follows below:

Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: h (x)= 3

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: What is the 1881th derivative of the function given by f(x)=1881x + 1923 at the point x=2020.

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