Ex.2 : Use first derivative , second derivative, and the graph y= x²-4 to asymptotes X-1

Q: The above is the graph of the derivative f '(x). How many critical points does the original function…

A: From the graph of function f'(x), number of roots of f'(x) are three. Let f'(x)=ax3+bx2+cx+d

Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

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Q: Find the equation of the function f whose graph passes through the point (0, 8/3) am whose…

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Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

A: Given a derivative of a continuous function y=f(x)

Q: Given function: y = x* – 4x3 +2

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Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Find the value of the derivative (if it exists) at the indicated extremum. -4 4/6 3 f(x) = - 3xVx +…

A: To find: The value of the derivative fx=-3xx+2. Formula used: Product rule of differentiation:…

Q: Graph the defined function over a one-period interval. y = - sin (x - pie/2)

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Q: Using the derivatives of In x, tell in a complete sentence why Inr is increasing, and why its graph…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Example: Sketch pictures of some functions that would not have a derivative at x = 2.

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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: If the slope of the tangent at any point of a function f passing through the point (2,-2) Is e^(-…

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Q: Graph ƒ(x) = x cos x and its second derivative together for 0 ≤ x ≤ 2π. Comment on the behavior of…

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Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

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Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

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Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: Graph ƒ(x) = x cos x and its second derivative together for 0<=x<=2pai. Comment on the…

A: We have to find it's first derivative .

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: Example 2: Find the equation of the tangent line to f (x) = when x = 1. V3x2+1

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Q: 4 -4 -3 2 4 -2

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2…

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Given the graph of derivative of f,

Q: Sketch the graph of the derivative for function shown.

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Q: et+1 g(æ) = x + 1

A: Given that gx=ex+1x+12To find : g'x Solution :…

Q: Each limit represents a derivative f '(a). Find f(x) and a.

A: Given :           The derivative of a function f at a number a is…

Q: Find the derivative.

A: Differentiate above equation with respect to x dydx=ddx{ln(x+1x3+1)}dydx=1(x+1x3+1)ddx(x+1x3+1)…

Q: Sketch the graph of the derivative for function shown.

A: Plot the derivative for -∞<x<0. The function f(x) is constant in the interval -∞<x<0 so…

Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Suppose the derivative of the function y​f(x) is (x-1)^2(x-5)(x-2). At what​ points, if​ any, does…

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Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

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Q: 3. Use the second derivative to find the location of all local maxima for the following function and…

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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: The graph shown is the 1st derivative of function where its domain is 20 10 8 2

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Q: Please show step-by-step solutions.

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Q: 1. Sketch a function that has a horizontal tangent line for all values of x. Explain how you arrived…

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

Q: If f(x) = 2x2 – x³, find f'(x), f"(x), f''(x), and f(4)(x). f'(x) = f"(x) = f'"'(x) = f(4)(x) =…

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Q: When looking at the graph of an original function, how do you know when the derivative of the…

A: To find the derivative, for your visualization, just draw the graph and the graph of its derivative.…

Q: 1 2 3. - 1

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Q: 7)Determine the points at which the graph of the function has a horizontal tangent line. flx) x2 х-1

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Q: Зх-2 2. Find the vertical and horizontal asymptotes for f(x) = V4x²+5'

A: As per guideline we can solve maximum one question you can repost other questions

Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: Find the equation of the function f whose graph passes through the point ( 0, and whose derivative…

A: We have to find value of f(x)

Q: 24. Consider the graph of y = Use limits and 1+ eax first derivatives to determine how the shape of…

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Q: (a) Find the derivative f'(x) of the function f(x) = (b) Graph f(x) and f'(x) side by side using…

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Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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Q: 10

A: The graph of derivative is made by observing the slope of given function

Q: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get

Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…

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.