1. Given the function f(x) = x2+4x-12/x2 a) Show your work for finding the derivative, to prove that f′ (x) = −4x+24/x3 b) Show your work for finding the second derivative to prove that f′′(x) = 8x−72/x4 c) Find the x and y intercept(s). d) Find the vertical asymptotes and determine the behavior near the asymptote(s). e) Find the horizontal asymptote.  f) Find the intervals of increase/decrease and any local maximum/minimum points. You must include a clear interval chart. g) Find the intervals of concavity and any points of inflection. You must include a clear interval chart.

Q: Function, f(x) Slope at x = 1 Derivative, f'(x) f(x) = x-0.7 2. f(x) = e*? 1.

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Q: how do you indicate the derivative with any method: g(t) = 3/t^5; estimate g'(1)

A: Write g(t) using negative exponents to get rid of the fraction. Then use exponent rule.…

Q: 1. Use limits to find the derivative of the following function at the point a = -1. 1 2x + 1 f(x)= =…

A: We have to find derivative

Q: (a) h(x) = x^√√x² +1 (b) f(x) = (3x² - 2x+1)³(x¹ -2r²- 3)² 4 (c) g(x) = (3-4) ¹ 5x+7

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x;…

A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

Q: 5 2. R(z) = 3. f(x) = V1-9x

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Q: Find the derivative of the function f(z), below. It may be to your advantage to simplify first. 28…

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Q: x+D メD

A: To Determine: we have a function then find the derivative Given: we have a function Z(x)=Hxx-D2+x2…

Q: 4. Given that g(x) = x^4 + x^3 − 3x^2 + 2, answer the following. (a)  g"(x) =  .............. (b)…

A: We have,  gx=x4+x3-3x2+2              ⋯⋯1 (a) By definition of derivative, ddxkxn=knxn-1 On…

Q: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

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Q: Q2. Use the definition of the derivative to find ý of the function y = sin(x). %3D

A: Here given function is  y = sin(x)

Q: Of the two functions f and g in Figure , which is the derivative of the other? Justify your answer.

A: Given Graph,

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: Given f(x)=(1-x)23  To find  Find left-hand limit derivatives from the left and from the right at x…

Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

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Q: The folowing is a reworded question from very last night . A printed solution of  a length of curve…

A: To find the correct integrand to evaluate the length

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: Given: fx=1-x23 To Find:  To find the left hand derivative LHD and right hand derivative RHD and to…

Q: The second derivative for the following function at x = 2 f(x) = V2x + is O 1 O 1/4 O 1/2 3/4

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Q: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

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Q: How to solve the derivative of this

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Q: The cost, in thousands of dollars, of airing X 30-second television commercials during a Super Bowl…

A: Note:- These are multiple sub parts question and according to our company guideline we can do…

Q: Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: fi fa>= 2 g. %3D 4X+1 3X-2 he fの= Wi fac) = X²+1 X3+1

A: There are multiple sub parts, As per company Policy I have answered first 3 subparts g.

Q: If f(x)= x2 +4 then what is the derivative off at x=-1? %3D Solo

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Q: Using the definition of the derivative, find f'(x) for the following function. 4. f(x) = - x2 + 8x -…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: The following is a step in the evaluation of the derivative of a function f(x) at a point x = 1…

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Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: y=x(tan^-1)(2x)-(1/4)ln(1+4x^2) find derivative of the function: full steps please

A: The given function is

Q: I need the third derivative for all of the following functions: f(x)= + 1 + x

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 3. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = tan (In(x) +x² –…

A: Trigonometris identities d/dx(tanx)=sec2x d/dx(in(x))=1/x d/dx(xn)=nxn-1 d/dx(sinh(x))=coshx…

Q: The following function is given: f(x) = x- 2x3 (a) What is the derivative of this function with…

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: 4 Find the derivative of the function f(x) = %3D x +7 Provide your answer below: f'(x) =

A: Given query is to find the derivative of the function.

Q: B) Find the Derivative by using the definition for the following 1-x function f(x) = 2x Then find…

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Q: 8.What is the derivative with respect to a of f(x) = (5 – x2)²? оА. (5 — а?) (5 — а*) O B. 2(5 – a?)…

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Q: Find the derivatives of the following functions. Do not simplify. (a) f(x) = ((3x−5)(−x^−2…

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Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

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Q: 4 f(x) (x2 - 4x)2

A: Givenf(x)=4(x2-4x)2or f(x)=4(x2-4x)-2

Q: 1. For the function f(x) = 3x? + 8x – 2, (a) Find the slope of f(x) at x = 3 | (b) Find equation of…

A: According to the bartleby guidelines, for more than one questions asked, only the 1st question…

Q: A) Consider the function f(x) whose second derivative is f’’(x)=4x+3sin(x). If f(0)=4 and f’(0)=4,…

A: According to the guidelines in case of multiple questions, We are only allowed to do first question.…

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: To compute the derivative of 2cosx with the chain rule by writing this function as a composition…

A: Consider the two functions f(u) and g(x). Find the composite function f(g(x)) and thus the outer…

Q: Compute the derivative of the function f(x) = S7+3x²' at the point 4, using the definition. Ex. 2.…

A: Derivative.

Q: Find the derivative of the function f(r), below It may be to your advantage to simplify before…

A: The given function is f(x)=ln(e-14x)

Q: What is the first derivative with respect to x of the function g(x)= 4/9 * О 4/9 O 4 O 12

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem)

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find f’ (x), i.e. the first derivative of the question below f (x) = (x - 4) (x – 1)

A: Topic:- derivatives

Q: In finding the root with Newton's Method, an initial guess Xo = 4 with f(Xo)= 1 leads to X1 = 3.…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: