Given the function こx (x+2)(x-2) yl"=-6x(x²-ax+4) (x+a)³ (X -1)³ 3. with 3 Complete the first deri vative Include all maximums and minimeims. Include all yntervals decreasing, on analysis. where is increasing constant.

Q: For the function, f(x) = 9x² – x³ - a. Use the derivative to find all critical points b. Classify…

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Q: Find the limit of the square root of (4x^(6)-x) over (x^(3)+3), as x approaches positive infinity

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Q: Find the critical points for the function in terms of b: Ax) = 3x-e

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Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

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Q: Find the minimum value of f (x) = 7x² – 2x + 4 on the interval (0, 1].

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Q: At what x-value is the global minimum for f(x)=x2−4x+3 within the interval  0≤x≤5?

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Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: Find the absolute extremd of the on the closed interval. 6x2 g(x) (-2, 1) X - 2 minimum (x, y)…

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Q: 2. Will the limit of all polynomial functions / (x) as x approaches a be always equal to the value…

A: Find your answer below

Q: Find the critical points of the function f(x) = 8x^3 + 4x^2 - 12x + 10 and determine their nature.

A: Solution: Given: f(x)=8x3+4x2-12x+10

Q: for what value of x does the function  f(x) = 1/3 x3 - 4x attain the absolute minimum in the…

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Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

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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: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

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Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

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Q: 3. What is the maximum value of the function f(x) = 2x- 2x + 6 in the interval %3D [0, 2]?

A: Introduction :

Q: What is the absolute minimum value of g(x)=−2x^2−2x−1 over [−3,4]?

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Q: f(x): 2x at x = 4 x2-3 f(x) = V3x - 10 at x = 2

A: According to question,a. Given function,fx = 2xx2 - 3

Q: Sketch the graph of y = (x² – 1)² – (2x – 1)². [In your answer, you must include the following: •…

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Q: Find the minimum value of the function f(x) = x³ – 6x² + 4x + 12 in the interval(-2,6] within 10% of…

A: We need to find minimum value.

Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: (5) Use the first derivative test to classify the critical numbers of the function s(r) = 2¹-4r³+17.…

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Q: The function Ax) = -2x(x - 1)(x - 2)(x+ 2) %3D has 4 zeros. has a maximum O as x→-∞, y–-∞ all of the…

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Q: Find the minimum and maximum of the function y = - 6480z on [-8, 8] by comparing values at the…

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Q: Find the absolute maximum and minimum assuming the function is f(x) = 2x^4 - 8x + 3 on interval…

A: f(x)=2x4-8x+3

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

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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: How to Find the quadratic function f(x)= ax2+bx+c that goes through (3,0) and has a local maximum at…

A: NOTE: Refresh your page if you can't see any equations. . the vertex form of the parabola is given…

Q: 4. Find the maximum of the function f(x) = 100-(10 – x1)? – (5 – x2)? by Simplex Method. Take…

A: Given function is fx=100-10-x12-5-x22 Let the coordinates be x1,x2 And given initial coordinates are…

Q: 1) Find the Absolute Maximum and Absolute Minimum for f(x) = x³ 9x² +24x on [0,5]

A: At absolute maximum and minimum of a function y=f(x), its first derivative is zero, i.e. f'(x)=0 (a)…

Q: for what value of x does the function f(x)=x^3-3x^2 attain absolute maximum in the internval (-1,4)

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Q: Where is there a local maximum on the graph of the piecewise function f(x) = 2x + 5 if x 8?

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Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: It is known by linear approximation that 1+xk=1+kx for the values of x near 0. The given function is…

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

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Q: Consider f(x) = xlnx on the interval [1,6]. When will the first derivative equal zero? For each…

A: Given that: f(x) = xlnx   x∈[1,6] To find: When will the first derivative  equal to zero. And for…

Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

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Q: Find the absolute maximum value of f(x)=3x^4−4x^3−12x^2+1 on the interval [−2,3]

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Q: identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x

A: y=(x+3)2/ e2x Or, y = (x+3)2e-2x We need to find it's derivative and equate the same to zero.

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: Suppose the derivative of a function is x2 + 2x -3. a) On which open interval/s is the function…

A: Consider the given: Given:f'x=x2+2x-3 Find the critical numbers: Substitute…

Q: If f(x) has a relative minimum value at x = 4, then f'(4) = 0 or f'(x) is undefined at x = 4 Select…

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Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

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Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

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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: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum…

A: Given: fx=x3+ax2+bx To find a, b such that function has local maxima at x = -1 and local minima x =…

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

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Q: Find the absolute maximum of h(x)=x2 −x−2 over [−3,6]. Enter only the y-coordinate of the maximum.

A: Determine the  derivative of the function  and find the critical points.