Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the critical points for the functions? E-what is f" evaluated at these critical points?

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

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Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: Given that the function is        f(x) = x e-x^2

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: Q-2: Find the derivative at each critical point and determine the local extreme values.

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Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

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Q: 4) Use logarithmic differentiation to find the derivative Of the given fünction.Show all steps.…

A: Consider the given function y=xx1+x24

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: SW Solve for the first derivative of ,(x+5) x' +e x³ +e + Vx f (x) = V0.1 at x= 0.05 using FCD BCD…

A: f'(0.05)=336.6222-333.90350.008=2.71870.008=339.8375 App value of f'=339.8375 exact value of…

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

Q: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: 7.) f (x)> (3x+2)(5x-2)

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

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Q: fcx)= Y文 メ ー^

A: Local extrema

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: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: We have two approaches to classifying critical points as local minima or maxima: the first…

A: To find the local minima and maxima we use both the first and second derivative test  for functions…

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. Specify whether…

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Q: f'(x) = (2x – 1)ee".

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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: 4. Find and classify the critical points of the given function by using Second Derivatives Test. 1 1…

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Q: Consider f (x) = x* – 8x2 + 1. a. Find the critical values. b. Use the first derivative test to…

A: We have , f(x) = x4 - 8x2 + 1.  To find : Critical Values.

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: he value x = ! is a critical number of the function f(x) = x ln(x), which has x) = 1+ ln(x). Use the…

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Q: Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x…

A: To find the first five derivatives of fx=e0.8x when x=24 using central divided difference…

Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: The given function is fx=9x2+7. Note that, the denominator of the above function is not 0 for any…

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: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

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: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Find the relative extrema of f(x) = 4+ 40x – 5x? using both first and second derivative tests. f (x)…

A: Explained below

Q: (1) For what value c on the interval [-10, 10] can the second derivative test be used?

A: Second derivative test is used to check if a critical point is a local minimum or maximum.  So we…

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

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