4. The graph of f(x) = -3(x – 2) – 6 is a parabola that with its vertex at _ is the (minimum/maximum). opens ( ), and f(2) = value of f.

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: Compute the abscissa of the minimum point of the curve  y = x3 - 12x -9.

A:

Q: 4. The graph of f(x) = -3(x – 2)² – 6 is a parabola that %3D opens with its vertex at (L, ), and…

A: Given: The function fx=-3x-22-6, To determine: The given blanks in the following statement, "The…

Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y x³ on the interval 0 0 and p and q are…

A: step:- 1 Generalization using nature of graph In interval (0,1) First draw graphs of x13,x12,x,x2,x3…

Q: Consider an arbitrary quadratic function f(x) = a.x² + bx +c where a, b, and c are constants with a…

A: We need to find second derivative test to check local maximum and minimum

Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: 4. cubic equation must have at least 1 real solution so it must have cut the x-axis once since if…

Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: In 2009, the federal income tax T on income of x dollars (up to $82,250) was determined by the…

A:

Q: find a cubic function f(x)=ax3+bx2+cx+d whose graph has a relative minimum at (0,1) and a relative…

A: Let the given cubic function

Q: Find the global maximum and global minimum of f(x)=x22x in the interval [−1,3].

A: We first find the critical points by solving f'(x)=0

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

A:

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: Consider the problem of finding the local minimum points of the function f(ï) = -4 +" over the…

A: Given

Q: Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local…

A:

Q: For a certain function, f'(x) = 0 and f' (x) > 0 for -1 < x < 2. Which statement is not true? a)…

A:

Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

A:

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

A:

Q: 1 Use the maximum-minimum principle 1 to Find absolute maximum and minimum Of the function: F(x)= x3…

A:

Q: SKetch the graph off over the indicaed Inteval and locate all absolut and relative maxımum and…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3. The graph of f(x) = 3(x – 2)² – 6 is a parabola that opens %3D with its vertex at (L, -), and…

A: The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If…

Q: 7  please answer, type the solution if you can please. or write clearly

A:

Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: 1. Suppose that f(x) = -ar/2 + bæ/2. Reparameterize this function in terms of the location of the…

A: given fx=-ax32+bx12 differentiate the function with respect to x f'x=-32ax32-1+12bx12-1…

Q: Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local…

A: We have to find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cxhas a…

Q: Find the global minimum of the function f (x) = 2x’ + 3x² – 12x + 4 on the interval [-4,2].

A:

Q: Find the second iteration value of an extremum (maximum/minimum value) of f(x) = 5sin2x - bx2 - cx…

A: Given the function fx=5sin2x-2x2-4x. The initial guesses are x1=0, x2=1, x3=1.5. The Quadratic…

Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: Q1- Find any local maximum and local minimum values and sketch the curve: x+ 1 S(x) x² – 1

A:

Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

A:

Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

Q: Find constants a and b so that the minimum for the parabola f (x) = x² + ax + b is at the point (4,…

A:

Q: I am stuck on the maximum and minimum values of y and corresponding x.  Will you please assist on…

A:

Q: 1. Find the absolute maximum and minimum of y = x³-3x² + 2, [-1, 3]. Sketch the graph.

A: Given function is y=x3-3x2+2

Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: Find the absolute meximum and absolul-e minimum of fcx) = X intereval [4,8] x- 48X Over the

A: From the given function; fx=x33+x2-48x First, we have to find the critical points; As we know that,…

Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

A:

Q: 3. Investigate the existence of local maximum and or minimum point(s) of the function f(x; y) =x -x…

A: Given: f(x, y)=13x3-x+xy2

Q: Find the value for x for which the graph of y =2e reaches its first minimum value.

A: To find the value for x for which the graph of below equation reaches its first minimum value.…

Q: 3) Find the abolute maximum and absolute minimum valuer of f(x) = x²-6x+5 %3D

A: using double derivative test

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: The graph of f(x) = -3(x – 2) – 6 is a parabola that орens with its vertex at ( ,), and f(2) = value…

A: fx=-3x-22-6 Comparing with fx=ax-h2+k, we get a=-3, h=2 &amp; k=-6. Now since a&lt;0, therefore the…

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

A:

Q: (4,28) is a maximum or a minimum point of the function g(x) = -x3 + 6x? – 4. Verify whether the…

A:

Q: 1. Explain how would you determine the maximum value of y= 1 3-cos x

A:

Q: Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.

A:

Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

A:

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

A:

Q: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

A: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

Q: The graph of f1x2  31x  222  6 is a parabola that opens, with its vertex at 1 , 2, and f122 is…

A: To find the graph of the given function                         f(x)=3x-22-6 and to find the vertex.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.