Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: -x²+5 < f (x) < x+1 2

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

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Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Use the second derivative test todetermine whether f(x)=-2x³+6x2-3 has a localmaximum or…

A: Given,          fx=-2x3+6x2-3

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

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: use the first derivative test to characterize each critical value of f(x)=x3+6x2-18x+3 as a maximum,…

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: show steps please

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Use the First Derivative Test to locate the x-value of all extrema. Classify if it is a relative…

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Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

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: . Find the local and absolute minima and maxima for the function over (-∞, ∞). 3 y = x³ (1-x)6

A: Given, y=x31-x6

Q: Use the second derivative test todetermine whether f(x)--+ 18z has a localmaximum or localminimum at…

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

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: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

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Q: Find all critical points of the function f(x)=5x5-2r and use the First Derivative Test to find local…

A: The given function is f(x)=5x45-2x

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: Determine the open interval(s) in which f(x) = 2x3 – 6x² is increasing or decreasing. Also, ocate…

A: Given        fx=2x3-6x2

Q: What is the absoluite extrema of the function h in interval [0, π]. Calculate and state the…

A: Exponential and sin, cos are always continuous

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

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Q: find all critical points of f(x) = x²e², and use the second derivative test to determine if each…

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

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Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: Function f(x) is defined as f(x) = x3 + 2x² - 20x + 10 in interval [-2, 1], what willI be it's…

A: Introduction :

Q: Show that |x + y|≥||x|−|y||, solution without using piecewise function

A: Just I have used the triangle inequality of absolute function and easily prove that the given…

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: the absolute minimum of f(x) = −x3 − 14x2 − 60x − 75 on interval [−7, −5]?

A: To find: The absolute minimum of fx=-x3-14x2-60x-75 in interval -7,-5. Calculation: The derivative…

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

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