8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

Q: 2) Consider the function g(x) = x3 + 3x2 – 9x + 2 on the interval [-4,2]. Find all local extrema,…

A: According to our company policy we can only answer the first question and rest of the questions can…

Q: For the function f (x) = 3x° – 5x* – 200x³ , find the critical value for f"(means find the x…

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Q: Find the absolute extrema of the function on the closed interval.                         f(x) = 2x3…

A: We find the critical points by solving f'(x)=0 -1 is not in the interval [0,3] 1 lies in [0,3]

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

A:

Q: Find the absolute extrema of the function on the closed interval.                   f(x) = x3 + 6x2…

A: To find the absolute extrema of the function on the closed interval. first differentiate and find…

Q: Find the global extrema of f(x)=√5−4x on the interval [−1,1].

A:

Q: 9. Show that for f(x) = x° we have f"(0) = 0 but the point x = 0 is not an inflection point of f.

A:

Q: Find the absolute extrema of the function on the closed interval.                          f(x) =…

A: The given function is Solve the absolute extrema on closed interval [0,4] by finding its derivative…

Q: Find the absolute extrema of the function on the closed interval.                          h(x) = 5…

A:

Q: 2) Consider the function g(x) = x³ + 3x2 - 9x + 2 on the interval [-4,2]. Find all local extrema,…

A:

Q: Find the absolute extrema of f(x) = x3 +5x2-8x+2 on the interval [−1, 2].

A: Given function is fx=x3+5x2-8x+2 ; x∈-1, 2

Q: 7 Determine a value for r so that h(x) x + rx² – 7x has an inflection point at x = 5. 2 -- |

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Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: )=x+- at x = C at x = 0

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Q: Please show steps.

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Q: Find all the critical numbers for the function f(x) = (x-1)/(x+1)

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

A: Relative extremum of a function are critical points of the function. Critical points of a function…

Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

A:

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: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: Find the critical point of the function f(x, y) = 8 – 4x + 7x² – 6y – y? - -

A:

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

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Q: Find the critical numbers of the function. f(x) = x³ + x?

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

A:

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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Q: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

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Q: The interval where  f(x) = )=(√x+2) / x2 - 2x - 8 is continuous is ?

A:

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

A: y = 3x2/3 − 2x,                                   [−1, 1]   absolute extrema of the function = ?…

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: Find the absolute extrema of f(x) = −x^(2) + 3x on the interval [0,3] .

A:

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: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

A:

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: 2. Find the absolute extrema of the function on the closed interval. f (x) = Vx – 2, [0,4]

A:

Q: Find the absolute extrema of f (x) = x-12x on the closed interval [0, 4].

A: The given function is, fx=x3-12x The interval is 0, 4

Q: Find all the critical points of the function f(x) = x^3 - 2x^2 - 15x + 2 on the interval [-1, 3]

A: Let's find.

Q: Find the absolute extrema of f(x) = 2x3+3x2−12x on the interval [0, 2]

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Q: Locate the absolute extrema of the function f(x)=x'-12x on the closed interval [0, 3].

A:

Q: Find the absolute extrema of f(x)=x^3-6x^2+5 on the interval [-3,5]

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Q: Find the absolute extrema for the function over the specified domain. y = x2 5 over [ – 1, 2] -

A:

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: Find the critical points of the function x + 1 f(x) = (5 – x)2 -

A:

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

A:

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: a) f(x)= x° (x – 4 )²

A: To find critical number of f(x)=x45(x-4)2

Q: 4. Find the absolute extrema (abs. max and min) of f (x) = x2 - 8x - 1 on the interval [1, 10].

A:

Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.