1-5 1 The function f graphed below is defined by a polyno- mial expression of degree 4. Use the graph to solve the exercises. y A 3 4. (a) A function value f(a) is a local maximum value of f if f(a) is the interval containing a. From the graph of f we see that there are two local maximum values of f: One local value of f on some open maximum is , and it occurs when x = 2; the other local maximum is. , and it occurs when x = (b) The function value f(a) is a local minimum value of f if f(a) is the containing a. From the graph of f we see that there is one local minimum value of f. The local minimum value value of f on some open interval is and it occurs when x =

Q: 4. At which points does the function f have absolute maximum or minimum, or local maximum or…

A: Sol:- From the Above graph , it is clear that ,

Q: d) A function with no absolute extrema but with a local minimum of -5 at x = 4 and a local maximum…

A: Follow the procedure given below.

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x+5 interval [0, 3]. on the

A: The function is given by fx = x3-12x+5 To evaluate : The absolute maximum and the absolute minimum…

Q: Every differentiable function y= f(x) defined on an open interval (a, b) has an absolute maximum and…

A: True

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: 3. Find the absolute maximum and absolute minimum values of f on the given interval. a. f(x) = 12 +…

A: This question is related to maxima and minima of functions, We will solve it using differentiation.

Q: Find the absolute maximum and absolute minimum of the function f(x,y) = y(sqrt(x)) - y^2 - x + 3y on…

A: follow next step

Q: (d) Any local minimum or local maximum of a function f must occur at a critical point of f. True…

A:

Q: 4) Let f(x) = x* – 2x -1 be defined on the interval [-1,3]. Find the maximums and the minimums.

A: The given function is defined  f(x) = x4 - 2x2 - 1 Over [-1,3] To find minimum and maximum value of…

Q: 2. For this question, you do not need to provide a formula for your function. Draw a graph f(æ)…

A: We have to draw a graph of a function in interval [-4,4] has  1) An absolute maximum at x=4  2) An…

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

A:

Q: Find the global maximum and minimum for the function on the closed interval. x + 1 f(x) - 1<x< 2 x²…

A: We have to find global maximum and minimum.

Q: False. For example, the maximum off (x) = x 2 + 1 on [l, 2] is 5, occurring at x = 2, but f' (2) #…

A: Given, the function f(x) = x2 + 1 on [1, 2], we have to check the maximum of the function on the…

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

A:

Q: 4. At which points does the function f have absolute maximum or minimum, or local maximum or…

A: Absolute minimum:- Minimum value of total function Absolute maximum:- Maximum value of total…

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

A:

Q: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

A:

Q: Give an explicit formula for a function which has a critical point which is neither a minimum nor a…

A: We have to choose function according to condation.

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. (a) Find the critical point(s) of the function f(x) = x2/3 on the interval -1,8| 2. (b) Use your…

A:

Q: If an odd function g(x) has a local minimum value at x = c, can anything be said about the value of…

A: Let g(x) is a odd function i.e. g(-x) = - g(x)

Q: If f'(x)= (x+3)(x- 2)°(x- 4) , then f(x) has | (a) a local minimum at x =2 (b) a local maximum at x…

A:

Q: 1. Find the absolute minimum and absolute maximum of the function f(x) = 2x-3x? on the closed…

A:

Q: Determine the critical points of the function  : f(x) = (x^2-1)^3 and identify absolute maximum and…

A: The critical point of a function fx is a point in the domain of the function, where the derivative…

Q: Find the absolute maximum and absolute minimum values of the function 8 f(z) = 2° +- on the interval…

A:

Q: 10. Determine the absolute minimum points given the function at the close interval [a, b] g(x) %3…

A: Given that g(x) = (x+2)^3 -1.   , [-3,0] g'(x) = 3(x+2)^2 Putting g'(x)=0 =&gt; 3(x+2)^2 =0 =&gt;…

Q: If f(x) is a continuous, odd function and f(c) is a relative maximum , then f(-c) is a relative…

A:

Q: 1. (a) Find the critical point(s) of the function f(x) on the interval -4,4. x2 +4 1. (b) Use your…

A: Critical point and the absolute minimum is determined as shown below

Q: Find the local extrama of f(x)=x²-8x+12 on a closed interval [-2,5] O a. minimum value at x =4 is -4…

A: Topic- application of derivatives

Q: Determine the values of constants​ a, b,​ c, and d so that f(x)=ax^3+bx^2+cx+d has a local maximum…

A: we have to determine the values of constants a,b,c and d so that fx=ax3+bx2+cx+d has a local maximum…

Q: Find the exact global maximum and minimum values of the function. 1 for x 0 f (x)x х If there is no…

A: Given,

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

A:

Q: 3. Determine the absolute maximum and absolute minimum on the interval [-1, 2] for the function…

A:

Q: If g is a differentiable function that g(x) less than zero for all real numbers x, and if f'(x)=…

A: To analyze the extreme values (if any) of the function f(x) under the given conditions

Q: 1) Find the absolute maximum and absolute minimum for f(x) = x* – 18x² – 2 on the closed interval…

A: To find absolute maxima and absolute minima for fx=x4-18x2-2;     x∈-2,4

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

A:

Q: 3. Find the absolute maximum and absolute minimum valves of f on the.given interval. 1 f(x)=x°…

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: snip

A: Given:                          fx=x+1x Differentiate f(x) with respect to x…

Q: 5. Suppose that f is a continuous function such that f(x) > 0 for all æ and f(0) = 4, 1 f'(x) > 0 if…

A:

Q: Can you help me step by step?

A: Since, the function f is an even function, so by definition of even function:

Q: 2) Find the absolute minimum value on (0,∞ ) for 4 f(x)= 5+x+

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: 1) Find the absolute maximum and absolute minimum for f(x) = x-3x-2 on the closed interval [-2, 11.

A:

Q: 11. The graph of a twice differentiable function, f(x), with a relative minimum at (–1, –2) is shown…

A:

Q: 2. Give an example of a function f: (0, 00) → K that is continuous and bounded but does not achieve…

A: It is an usual example which derivative not vanish anywhere

Q: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

A:

Q: c) A function with an absolute minimum at (4, -3) and a local maximum at (-2,6) 6- 4- 2- -4 d) A…

A:

Q: 7. Find the absolute maximum and absolute minimum values of f(x)=2x-322/3 on the interval (-1,2]).

A: