Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.   f(x)=x^2−8x−6​; [2,5]

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

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Q: Evaluate the second derivative at this critical number.

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Q: At the point (1, 2),the function ƒ(x, y) has a derivative of 2 in the direction toward(2, 2) and a…

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Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

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Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 7 – x, - [-4, 4] minimum…

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Q: please take the first and second derivative of this function:    cube root of x^2 - (1/cube root of…

A: First express the expression with exponents of x.

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Explain how to find the critical numbers of a function.

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Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: Find the absolute maximum and minimum values of f on the given interval. f(x)= (cube root of x)…

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Q: Use second derivative test, If x3 f(x) = 25x + 5 then f(x) has a 3 local maximum at the point x = -3…

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: The limit of the function as x approaches 1 from the left is ... (0/1 Point) 6- 4- 2 -10 -5 5 10 -2-…

A: Given-  To Find- The value of the limit of the function as x approches 1 from the left hand limit.

Q: Find the equation of the tangent line at (3, f (3)) when f (3) = 20 and f' (3) = 4. (Use symbolic…

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Q: Consider the function defined on the indicated interval. f(x) = 2a° – 18x2 + 48x – 36, [3, 6] Find…

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Q: Find the absolute extrema of the function on the closed interval.

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=3−16xf(x)=3-16x, and the line…

A: GIVEN DATA: Triangle is bounded by the equation of line fx=3-16x                         line…

Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

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

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Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: (f°9)(x) if f(x)=2x3 +1 and g(x)=6x +5

A: We have to find the composition of the function then have to find the second order derivative.

Q: 1. f(x)=(2x-5) ¹ (4x+3)²

A: We need to find derivative.

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx *please explain step by…

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Q: Find the slope of the tangent line of the function g(x)=3-x^2 at the point (2, -1)

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Q: The second derivative has already been found and factored to be f"(x) = (5x)(x+2). Use interval…

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Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: The function f that has the given derivative f'x=sec22x and passing through point π2,2. Now,…

Q: At what points are the functions continuous x -X- g(x) = X - 3 y " 5, x = 3

A: Given:  1. 2.

Q: If we have to integrate a function, what is the first thing come into our mind?

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Q: At the point x 2, the function -8 2<x<* f(x) = |x-2 -< xs2 is (a) continuous and differentiable (b)…

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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: Vx-3 6. f(x) = X-9

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Q: How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

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Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 4x − 5x2…

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Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: (-3,3) Homework f(x) G5,1), Evauate (4,-2) -- ,f(x)dx

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Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: Find the slope and an equation of the tangent line to the graph of the function f at the specified…

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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: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) &gt; 0  from graph  Function is increasing…

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…

Q: Find the approximate root of the function f(x) = x^3 - x - 9 in the interval [-3,3] for 2 iterations…

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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.