What is the absolute maximum value of f(x)= x^3-3x^2+1 on [-1,6]

Q: The lower limit is less than 0, so part two of the fundamental theorem of calculus cannot be…

A: The second part of the fundamental theorem of calculus states If f(x) is a continuous function on…

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

A:

Q: Identify the absolute minimum of f(x)=2x2 +x+1 over [−2,3].

A: The given function is f(x) =2x^2+x+1 over the [-2,3].

Q: Consider the function f(x) = 2x3 - 6x2 - 18x + 9 on the interval [-2,4]. What is the absolute…

A: Given function - f(x) = 2x3-6x2-18x+9Differentiating f(x) with respect to x - f'(x) =…

Q: Sketch the graph of the function f that is continuous on [-1,4] and has the given properties: An…

A: Given information Function fx is continuous on -1,4 Function fx has an absolute minimum at 4…

Q: Sketch the graph of a continuous function on (0, 4) with aminimum value but no maximum value.

A: Given: The interval of a continuous function is (0,4)

Q: Find any local maximum & local minimum  of f(x)=-0.4x3-0.6x2+3x-4 on the interval (-6,4)

A:

Q: Describe the procedure for finding critical points of a function in two independent variables

A: Based on the theorem on location of extrema, our strategy is to Find fxx,y and fyx,y, if the exist,…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12…

A:

Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

A:

Q: What is the absolute minimum value of q(x)=2x2−1 over [−2,5]?

A: Take the derivative of the given function and equate to zero and solve for x.

Q: Use finite approximations to estimate the under the graph of the function f(x) = 4 – x² between x =…

A: Here given that a function and find lower sum with four rectangles of equal width. Here i attached…

Q: Determine whether the following statement is true or false, and explain why. The absolute maximum of…

A:

Q: Find the maximum value of f(x) = 6x +1 - x on the horizontal span of 0 to 6. (Round your answer to…

A: Just use second derivative test.

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: Find the absolute maximum and minimum values of f on the given interval. f(x)= (cube root of x)…

A:

Q: Find a finite difference approximation to f"(x) using the points x — x − 2h, x-h, x,x+h,x+2h and…

A:

Q: Sketch the graph of a function on [-1, 2] that has anabsolute maximum but no absolute minimum.

A: According to the given information, it is required to sketch the graph of the function on [-1,2]…

Q: Draw the graph of a function that's defined everywhere on the interva: [0, 5] that has an absolute…

A:

Q: Differentiate the function. 3. %3D In(x)

A: Given y=3ln(x)differeniatey'=ddx3lnxy'=3ddx1lnxApply exponent rule:  1a=a-1y'=3ddxln-1xApply chain…

Q: What is the average rate of change of the functin g(x) = 2x^2 -9 on the interval [4,7]

A: g(x)=2x2-9 on the interval [4,7]

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14…

A: To find: The expression for the volume V of the box in the form of x. Given: The dimension of the…

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

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. absolute…

A: Given problem:- Sketch the graph of a function f that is continuous on [1, 5] and has the given…

Q: Find the absolute maximum and absolute minimum of the function on the interval. f (x) = 5(x² -4)/z³,…

A:

Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: Sketch the graph of a function that has a local maximumat 2 and is differentiable at 2.

A: We have to sketch graph of function that has local maximum at 2 and is differentiable at 2. We know…

Q: Give an example of a function that is not Riemann integrable.

A: To give example of a function that is not Riemann integrable :-

Q: . What does it mean to say that f142 is a local maximum valueof f

A: Given :            f(4) is a local maximum value of f.

Q: If f is continous on[0,1] then f has an absolute maximum on (0,1)   True or false?

A: We will do it by a counter example.

Q: Determine all critical points for the function. 2) f(x) = 45x3 - 3x5 %3D

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

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

A:

Q: Estimate the absolute maximum value of the function y = x3x-x to two decimal places on the interval…

A: Please see the explanation below

Q: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

A: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

Q: Sketch the graph of a function that has a local maximumat 2 and is continuous but not differentiable…

A: Definition used -        Absolute value functions-            The absolute value function has a…

Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x – 2…

A:

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11…

A:

Q: (3) Construct a function defined on the closed interval [0, 1] with no maximum and minimum. Justify…

A: The Extreme Value Theorem (EVT) says: If a function f is continuous on the closed interval a ≤ x ≤…

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: A function f defined on [a, b] always has an absolute maximum and absolute minimum on [a, b].…

A: False

Q: Function f(x) is defined as f(x) = x3 + 2x² - 20x + 10 in interval [-2, 1], what willI be it's…

A: Introduction :

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: = -3x^2 + 10x on the interval [1, 3] occur. Absolute maximum occurs at x = Absolute minimum occurs…

A:

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

Q: Suppose you find the linear approximation to a differentiablefunction at a local maximum of that…

A: It is known that the linear approximation of a differentiablefunction at a local maximum of that…

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

A:

Q: By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the…

A: