In(x) Find the maximum and minimum values of the function f(x) on the interval [1,6]. = The minimum value = The maximum value

Q: Let f(x) = x² – 8x – 14 Use the second derivative test to find any local maxima and minima. First,…

A: for critical value put first derivative zero if second derivative positive minima and if negative…

Q: The derivative of the function f is defined by f'(x)=x²-3 sin (x - 5). What is the x-coordinate of…

A: Solution:

Q: f(x)=(x^3-25x)/(7x^2+1) Use the first derivative test to find the critical points.

A: Given: The function, fx=x3-25x7x2+1.

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. x²…

A:

Q: Find the maximum and minimum value of the function f(x) = xe¯¤ on the interval (0, 2]. %3D

A: If you like the solution then please give it a thumbs up.. The Answer is:        Maximum value = 1…

Q: Perform a first derivative test on the function f(x) = /x In 4x; (0,0o). a. Locate the critical…

A: Given functionfx  =x ln4x     ; 0,∞

Q: The function f(x) = 2x3 – 42x? + 240x + 1 has derivative f'(x) = 6x² – 84x + 240. f(x) has one local…

A:

Q: Use second derivative test, If f(x) = 4x +9 then f(x) has a local maximum at the point 3. I= 3 I =…

A:

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: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

A:

Q: Find the absolute maximum and minimum values of f(x) = xe-x on the interval [0, 3].

A: Here, f(x) = xe-x on [0,3]   Extreme Value Theorem(EVT):  If a function f is continuous on a closed…

Q: 1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) =…

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Q: Find the absolute maximum value for f (x) = x'e¯ on the interval [-1, 3].

A: We can find the absolute maximum value using the application of derivative as below.

Q: Hi, I need help with this step-by-step. Please.

A:

Q: 3 + 3x – 5 Find the local maximum by solving the derivative P'(x)=0, – 2x + -- %3D |

A: Given Find out local maximum

Q: The function f(x) = 2a* - 39x2 + 240x + 10 has derivative f'(x) = 6x² – 78x + 240. f(x) has one…

A:

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

A: Given  The function  is  ƒ(x) = x2 + 3 on ⌈-3, 2⌉

Q: Plot f (x) = 2√x − x on [0, 4] and determine the maximum value graphically. Then verify your answer…

A:

Q: Find the x-coordinates of the absolute extrema of f(x) = -x² + 7x on the interval [1, 7]. Absolute…

A: f(x)=-x2+7x differentiating both side f'(x)=-2x+7 now f'(x)=0 -2x+7=0 x=3.5 So x=1, 3.5, 7

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: Find the absolute maximum and absolute minimum of - x2. f(x) = + x² – 15x over the interval [1, 5].…

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Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: The critical points of the function are the points where the function is defined but its first…

Q: Find the absolute maximum and absolute minimum values of the function  f(x)=x+4x on the interval…

A:

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

A: Given ƒ(x) = 2x3 + 3x2 - 12x + 1 on ⌊-2, 4⌋ (a) Find the critical points first dfdx=6x2+6x-12 Put…

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: We will do partial fraction and find out local Maxima points.

Q: 8. Using the second derivative test, find the maximum and minimum points for the function f(x)-x*…

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Q: 2. Find the absolute minimum and maximum of the function f (x) = – 2.22 on the interval [-2, 1).

A: We have to solve

Q: Find the absolute maximum and absolute minimum f(x) = + x2 24x over the interval 2, 6|. -

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Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

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: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: 7. Determine the absolute maximum and absolute minimum on the interval [-1, 2] for the function…

A:

Q: 9. Given the function f (x) = 3x -4x2 + 2, use the first and second derivative tests to find: a) the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

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

A: the given function is: f(x)=-x3+9x the given interval is [-4,3] (a) we have to locate the critical…

Q: 8. Using the second derivative test, find the maximum and minimum points for the function f(x)=x*…

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Q: Find the relative extrema of f(x) = 9+30x – 3x? using both first and second derivative tests. f(x)…

A: A detailed solution is given below.

Q: Find the absolute maximum and minimum values of the function g(x) = 2x− 4sin(x) on the interval [0,…

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Q: Find the absolute maximum and absolute minimum values for the function f(x) = x lnx on the interval…

A:

Q: The function f (x) 2x3 – 39x + 216x + 2 has derivative f'(x) = 6x? 78x + 216. f(x) has one local…

A: Function will have a local minimum at a point where the value of the derivative of the function will…

Q: Find the absolute maximum and absolute minimum values of the function f(x) = −x3 + 3x + 7 on the…

A: We find critical points by setting f'(x)=0 x=1 is not in the interval [-2,0]

Q: ve maximum or

A: Maxima and minima: Let f(x)=e3x2+4 For maxima or minima we need to find those values where f'(x)=0.…

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

A: Given fx=x4-x2 on -2, 2

Q: Use second derivative test, If f(x) = 4x+4 then f(1) has a local maximum at the point I = -3 I = -2…

A:

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: Use the first derivative to find all critical points and use the second derivative to find all…

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Q: The function f(x) = 2x³ − 33x² + 60x + 8 has derivative f'(x) = 6x² f(x) has one local minimum and…

A: Explanation of the answer is as follows