| B4(a): Verify Mean value theorem for the function f(x) = 5x° +T+2 over the interval [0, 1]. %3D B4(b): A ball is dropped from certain height, its position at time t is s(t) = -3t2 + 75 find the time t when ball hits the ground.

Q: increasing and decreasing. 5) f(x) = -x² +4 fx) -4 위

A: Given :  f (x) = - x 2 + 4    To determine : The intervals on which f (x) is increasing or…

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

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Q: Q2 (a) Let f (x) = x* - 4x³ + 10 (i) Find all critical points of f(x). Determine whether the…

A: For, critical points we take f'(x) =0 For, inflection points we take f''(x) =0

Q: Find all relative extrema in the function k(x) = (x2 – 4)-2 on the interval [-3, 3].

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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: Find the intervals on which the function y=xx(x&gt;0) is increasing and decreasing.

A: We take ln on both sides of the function

Q: 3x-1 Find the critical points of the function f (x) = x+6

A: Here the given Any point x is said to be a critical point of the function f(x) if f(x) is not…

Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: 3. Find the c value(s) that satisfy the Mean Value Theorem for the function f (x) = x² + 5x on the…

A: Note- As per our guidelines we are supposed to answer only one question at a time. So I am solving…

Q: if y=x to the 3rd power - 3x. find the maximum value of y? -1

A: Given

Q: 22 If Sx) is an odd function, the second difference [SSAx) – 2(0) +-Ax)]/(Ax)? exactly equals f"(0)…

A: Please check step 2 for the solution.

Q: At a certain vineyard it is found that each grape vine produces about 10 lbs of grapes in a season…

A: To find the number of vines that should be planted to maximize grape production.

Q: The profit function of a certain firm is f(x) = -6x² + 1188x - 1200, where x denotes units of…

A: The profit function is fx=-6x2+1188x-1200 Here, x is the number of units produced. Part a We need to…

Q: Find a formula for the linear function f(x) with slope 2 and vertical intercept 1. f(x) =

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Q: If a rock is dropped from a height of 100 ft, its position t seconds after it is dropped until it…

A:

Q: Find the critical points of the function f(K)-7x2-14x.

A:

Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

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Q: The path of a diver is modeled by 24 *+ 13 f(x) = - where f(x) is the height (in feet) and x is the…

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Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: The function y = has a: a) local max of % b) absolute max of % c) local min of % d) absolute min of…

A: The given function is: y=1x2+4

Q: Find the absolute extreme values of the function on the interval. 3) f(x) = In (-x), -5 s x s -1

A:

Q: (A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second…

A: y = x33-x+5y' = 3x23-1y' = x2 -1x2-1 = 0x2 = 1x = ±1

Q: #30) tind the critical mumbers of the function. f(x)=x² +6x² - 15.

A: Derivative the function and then equate to 0 find the values of x

Q: Find the absolute maximum of the function f(x) = x-x-x On the interval - 10 sxS2 (a) 14 (b) 13 (e)…

A: To find absolute maximum and minimu , first, we need to find critical points. These are the points…

Q: Consider the function f (x) = -x² + 10. Find the average rate of change in the interval -5 <x < -1.

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Q: At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season…

A:

Q: Q. 4 Find the absolute maximum and minimum values of f(x) = x³ + 5x2 – 7x over the closed interval…

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Q: 1. Find all local max/local min values of f(r) = x² – 6x – 1

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Q3. At what points are the functions continuous y =-3x x+3 y = x2-3x-10' y = (2x - 1) X-2

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Describe the long run behavior of f(t) = – 2(5)' – 3 | As t → - 0, f(t) → ? v As t → 0, f(t) → ? v

A: The function of the form f(x)=ax, where a&gt;0 is said to an exponential function. The exponential…

Q: Q2:Find all critical points of the function f(x)=(3x)/[(x^2)+9] Final answers should be ordered…

A: To evaluate the critical point of the following function  f(x) = 3xx2+9

Q: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a…

A: Given model of the equation is simplified by expanding the brackets:

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

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Q: At what value of x does the local max of f(x) occur?

A: Given, fx=∫0xt2-491+cos2tdt

Q: Find the critical number of the function. g(t) - | 2t - 5| t =

A: Given,    g(t) = | 2t-5 |   For critical points,  Make modulus to zero.    So,  2t - 5 = 0 t = 5/2

Q: A company produces chocolate Easter bunnies at a cost per unit of 0.60 + 0.005x dollars, where x is…

A: The cost function per chocolate bunnies is 0.60 + 0.005x in dollars and x be the number of item…

Q: 4. Find the absolute max and min of f(r) = 2+5x - x* on the interval [0, 4 ]

A: Calculate the value of function at local extremum point and end points of interval.

Q: Let p=(12-2x)^2 for 0≤x≤3 be the price at which x hundred units of a certain commodity will be sold,…

A: Given: P=(12-2x)2         for 0≤x≤3            Revenue   R(x)=xP(x) then    R(x)=x12-2x2…

Q: The sales of a product produces revenue R(x) where x represents the amount spent on advertising.…

A: Solution :-

Q: 4. a) Find the value of x where the function f(x) = (x – 4)3 is not differentiable.

A: According to power rule of differentiation , .

Q: The interval in which the given function is decreasing is at 3 points y = x3 – x2 – 5x - 4 (-00, -1)…

A:

Q: B3(a): Find the critical points of the fifuncținn f(x) = 4x³ – 48x + 4. (b): Verify the Mean value…

A: (a).   The given function is: f(x)=4x3-48x+4

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: Describe the long run behavior of f(t) : - 4 3: As t → - 0, f(t) → ? As t → 00, f(t) → ? v

A: We will use concept of limit to answer the problem.

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 pesos)…

A: To find: The number of item sold to maximize the revenue R. Given: The demand function is . Formula…

Q: According to the Florida Agency for Workforce, the monthly average number of unemployment claims in…

A:

Q: The population of the United States can be modeled by the function p(x) = 80.21e131x where x is the…

A: We have to graph P(x) and predict population in given years.   According to our guidelines we can…