x'-125 3- If f(x) : x-5 is the function continuous at x=5

Q: List the intervals of concavity for f(x) if it has a second derivative of f'(x) = (x +2)(8x - 25).…

A: The given second-order derivative is: f''(x)=(x+2)(8x-25) So, f is concave upward if:…

Q: 1. Using the First Derivative Test, explain why the function f(x) =-2x has no extrema on any open…

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: Apply the second derivative test to find all relative extrema. - 5)² (a) f(x)=(x

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Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: The derivative of a certain continuous and differentiable function is given by: y = 3-x - 12-x +9.…

A: For maxima-minima, derivative of the function must be zero. That is,…

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: 75. F(x) has a negative derivative over (-, 2) and (5,9) and a positive derivative over (2, 5) and…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Give an example of a function that is continuous but differentiable at x=2

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Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

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Q: Give an example of a function that is continuous on −∞ < x < ∞, but has NO DERIVATIVE at x = 3.

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Q: The function f is defined by f(x)=x/(x+2). What points (x, y) on the graph of f have the property…

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Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

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: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Prove that constant function is differentiable at ever x ER.

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

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: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: 3. Suppose a car travels at a constant rate of 70 kph for 2 hours and travels 55 kph thereafter.…

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

Q: If f(x) = x + 4 determine the intervals where f is increasing, decreasing, x +1' use the…

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Q: If a function is continuous and differentiable then its derivative continuous? True O False

A: A function, y=f(x) is continuous, if there are no holes or jumps in the graph of y=f(x) .

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

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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: 13. Suppose a continuous function f and its derivative f' have values table. Given that f(1) 2, use…

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: 5. Use the Second Derivative Test to find all local extrema of the function below. (3 points total)…

A: To find the local extrema of the given function f(x)=x4-4x3+2

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

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Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

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Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

A: We have to find the value of derivative of the function f(x) = 16 - |x| at the extremum point…

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

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: