14. Find the absolute maximum and the absolute minimum of f (x) = -x³ + 9x on [-4, 3].

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

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: Find the absolute maximum value of f(x) = x² – 2x + 8 over the interval [0,5|

A: The objective of the question is determine the absolute maximum value of the given function.

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: 4) Find the critical points of the function f(x) = x²- 9 x* + 15x +3 and identify their nature. Draw…

A: Given that: f(x)=x3-9x2+15x+3 The graph is shown below

Q: Consider the function f(x) = 4 – 5x", – 3 < x < 2. - - The absolute maximum value is and this occurs…

A:

Q: 3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: suppose f(x)’=x^4+x^3-6x^2. Determine the value of x where f has a relative minimum value.

A:

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

A:

Q: Find the absolute minimum maximum if they exist for f(x) = x+ 4/x

A:

Q: Suppose f'(x) =x++x³ – 6x². Determine the value of x where f has a relative minimum value.

A:

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

A:

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 maximum value of f(x) = x² – 2x + 12 over the interval [0, 4]

A: Use critical value and end points for absolute maxima and absolute minima.

Q: Find the absolute maximum and minimum values of ƒ(x) = x2 on[-2, 1].

A: Given,  fx=x2 on −2,1

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

A: Consider the given function.

Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: 2. Find the minimum value of f(x) = %3D

A: We expert are supposed to do first question . We have to find minimum value

Q: Suppose that f(æ, y) = x² – xy+ y² – 5æ + 5y with æ² + y² < 5?. 1. Absolute minimum of f(x, y) is 2.…

A:

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

A:

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 the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

A:

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: Find the absolute minimum value of f() = xe on [-5,0].

A:

Q: Find the absolute minimum and absolute maximum for y = x3 – -+ 4x +1 on [-2,2].

A:

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: Suppose f:(x)=x++x³- 6r2. Determine the value of x where f has a relative minimum value. O x=2 O x=0…

A: Function f'(x)=x4+x3-6x2 To find x where f has a relative minimum value

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval (0, 4]|

A: The absolute vale in the interval [0,4] for f(x) will be either at critical points or at end points.

Q: Find the absolute minimum value on (0,∞​) for f(x)=x − 1/x + 14/x^3.

A:

Q: Find the absolute minimum and absolute maximum of the function f(x) = (x2 − 1)3 defined on the…

A:

Q: Suppose f'(x) =x++x³- 6x². Determine the value of x where f has a relative minimum value. x= - 3 O…

A:

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

A: Find first derivative.

Q: ind the absolute maximum and absolute minimum value of f(x) = 12 + 4x – x on [0, 5)

A:

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

A:

Q: -, Determine the location and values of the absolute maximum and absolute minimum for the given…

A:

Q: 10. If the minimum of the function y =x 2 –4x+21 occurs at x =2, what are the coordinates of the…

A: In the question , it is already given that minimum is occurring at x = 2 So, just put the value x =…

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 minimum absolute extremum as well as all values of x where it occurs on the specified…

A:

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 5]

A:

Q: Find the absolute minimum if exists of f(x)=6x^2 −x^3 +8 on the interval 0≤x≤4

A: Use the first and second derivative test and find the absolute minimum of function f(x).

Q: 2. Find the absolute maximum value and the absolute minimum value of the function 3 f (x) : 5 – x2…

A:

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

A:

Q: Find the absolute maximum value of f(x) = x2 – 2x + 18 over the interval [0, 5]

A:

Q: Let f(x)=kx^-1+x^2 For what values of k, function f(x) has a relative minimum but not a relative…

A:

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

A:

Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

A: