11. f(x)=-x'+ 2x? |(a) Find the open intervals on which f(x) is increasing and decreasing. |(b) Identify the function's local and absolute extreme values, if any, saying where they occur.

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

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Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

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Q: 1. Find the equation of the tangent line of f(x) at the given point. f (x) = 6x – x2, (1,5)…

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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: Provide an example of a function f(x) which has all of the following properties: - it is periodic…

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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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: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: The function K has one critical point at 1 = 0. Use a number line and the first derivative test to…

A: We will solve the following.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: In the given question as follows, (a) find the critical numbers of f, if any, (b) find the open…

A: The critical numbers of a function are the values at which the derivative of the function is 0 or…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

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Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose we wish to compute the value of the continuous function f(x) for a given value of x. This is…

A: Solution: Explanation of equation (7.117) in the book: Given y=fx    ......(1) Now, (in the book)…

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=xlnx Differentiating with respect to x, we get f/x=dxdxlnx+dlnxdxx    Because,…

Q: Suppose h is a twice-differentiable function such that it has second derivative given by the formula…

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Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: 1. Evaluate. a) lim x--2 ³-2x² +12 x² +1 x² -8x+7 b) lim x-7 2. What is the average rate of change…

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Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

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Q: Find the critical numbers for function f(x)=x-3 ln(x)

A: Given function:  fx=x-3lnx

Q: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

Q: Given the following derivative = F’(x)=(x+1)(x-1)^3(x+2)^2 with critical values x=-1,1,2,-2. Where…

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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: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Use the first derivative test to find the critical points, local max and local min points (need y…

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Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

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Q: 5. Find the critical numbers, and the intervals of increase/decrease for y=ln(4-x) %3D

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

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: Sketch the graph of the function. Label all the critical points and show how you find them. h(x) =…

A: Given: The function is h(x)=log4(x-1)+3 To determine: The graph of the function and the critical…

Q: The graph of the first derivative of a function is shown a) How can we know in which intervals the…

A: Here we have the graph of the first derivative of a function is shown.

Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Find the critical numbers of the function  f(x) = 4x - tan x

A: fx=4x-tanx Differentiating with respect to x, we get f'x=41-sec2x=4-sec2x

Q: 4 Determine the set of x-values where f(x) 12z is continuous, using interval notation. (-x,5) u (…

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Q: 24. Estimate instantaneous rate of change of each function at the given x value using a centered…

A: Given :-  The instantaneous rate of change of each function at the given x value using a centred…

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

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Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

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

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Q: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.