3 Find the values of constants a, b, and c so that the graph of y = ax³ + bx² + cx has a local maximum at x = 4, local minimum at x = -2, and inflection point at (1,26). a= b= C= ***

Q: Solve the initial value problem for x as a function of t.. (t²-19t+90) dx dt x(t) = (Type an exact…

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Q: Let a = 7i+j and b - 67 - 7j. Find a - b .

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Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: e-1 Find the limit limä→0 tan x

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Q: h(x)=5.5x-3.42

A: We have given a polynomial  hx=5.5x-3.42 Leading term =5.5x

Q: Find the derivate of the function F(x) = x²(x²-8) a) C 2 6b) f(x) = (5x²³²-7) (6x + 1) F'(x) = c) 5…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 4. Consider the graph to the right, containing the points (0, 1) and (1, 5). A. What function is…

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Q: Find the volume of a pyramid with height 28 and rectangular base with dimensions 5 and 7 using…

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Q: Answer the following True or False. If f(x) is a positive 1-1 function with inverse f−¹(x) with f(a)…

A: Given:-fx is a positive 1-1 fuunction with inverse f-1x with fa=c,fb=dthen π∫abfx2dx=2π∫cdyb-f-1ydy

Q: question

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Q: If f(x) = 3x5 - 10x³ +5, on what intervals is f"(x) > 0? Enter the (disjoint) interval(s) below…

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Q: A plate in the shape of an isosceles triangle with base 1 m and height 8 m is submerged vertically…

A: A plate in the shape of an isosceles triangle with base 1 m and height 8 m is submerged vertically…

Q: given by C(x) = -0.07x² + 75x. Find C(288) C(287) Interpret the result

A: we will find the required.

Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = t² + 3t.…

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Q: = Evaluate d5 dx5 [x³ − 3x + 1]. (a) (3x² - 3)5 (b) 0 (c) 72 (d) 6

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Q: 2) Sketch the graph of a continuous function y = f(x) that satisfies the following (Identify any…

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Q: Complete the parametric equations of the line through the point (-1,-8,-7) and perpendicula plane -…

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Q: Given f(x, y) = 100x + 80y - 2x²- 4y² - xy Evaluate f(10, 9)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the slope at x = 3 on the graph of 2y - 4x = 9. (a) -4 (b) 2 (c) 10.5 (d) 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the 7+x…

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Q: Find the absolute maximum and absolute minimum values of the function over each of the indicated…

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Q: Q12 Construct the equation of the line passing through (0, -2) and (3,5).

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Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Find the limit. lim X→0 sin (8x) 7x

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Q: Find the derivate of the functions: a) F(x) = -3x²=4 : f'(x) = b) g(v) = 3 g'(v) = 2√² +5V-9 c) f(x)…

A: We need to find out the derivatives of the given functions.

Q: 3. Evaluate the limit for the graph: lim f(x). x+1* y 4 2 01 -2 2 48 x

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Q: An open-top rectangular box is being constructed to hold a volume of 350 in³. The base of the box is…

A: Given: volume = 350 in³ base material costing = 6 cents/in² front cost = 12 cents/in² remainder…

Q: Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar…

A: To change the Cartesian integral ∫-55∫025-x2 dy dx into an equivalent polar integral. Then to…

Q: The region bounded by f(x) = −4x² + 16x + 84, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: 3. Use the Gizmo to experiment with more functions of the form y = b*. Select the Show probe and…

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Q: [√² √sec²z - 1

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Q: - 49 -dx = X (Type an expression using x as the variable.)

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Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

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Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = y=(√x)⁹x

A: The given function is: y=x9x

Q: Find the volume of the solid generated by rotating about the x-axis the region bounded by y = 2.3*,…

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Q: Average Cost for Producing MP3s The average cost (in dollars) incurred by a media company each week…

A: Here is the solution:

Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: Find the tangent plane to the equation z = -4x² + 3y² - 5y at the point (3, 2, -34)

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Q: 15 sin ¹√2x dx = [

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Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

A: We have to find m'(-1) and n'(6) Where m(x)=f(x).g(x)        n(x)=g(x)/h(x)

Q: The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you…

A: Given f( x ) is continuous in the given domain If a function is continuois at x = a then limx→a-f( x…

Q: Determine the average rate of change of the function over the domain graphed. (-3,5). y (3,5) 41 2…

A: From the given graph  of the function f(x)   The function is defined for the interval [-3,3]   To…

Q: A vector with magnitude 4 points in a direction 340 degrees counterclockwise from the positive x…

A: let vector =V given  magnitude=V=4and direction=θ=340°now Vector V=<x,y>=?…

Q: Find the average rate of change of f(x) = x² from x = 1 to x = 4. (a) 3 (b) 5 (c) 15 (d) 6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The graph of y=f(x) has f(5) = 1, f(x) has f(5) = 1, f'(5) = -1, and f(5) = -1-

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Q: 4. Evaluate the limit, if it exists: lim x+1 a. 1 b. -1 x²-3x+2 x-1 c. d. 0 does not exist

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Q: A volume is described as follows: 1. the base is the region bounded by y = e³.5x, y = 3.5x² + 0.9…

A: Given,             A volume is described as follows:             1. the base is the region bounded…

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

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Q: Suppose a product's cost function is given by - 3q² + 800q, where C(q) is in dollars and q is the…

A: The details solution of the given question is given below in step 2.

Q: 3. Find the centroid (, y) of the region bounded by y = 2 cos(3x) and y = 2 sin(3x) from z = 0 to z…

A: Centroid is given by x¯=1A∫abxf1(x)-f2(x)dx and y¯=1A∫ab12f1(x)2-f2(x)2dx where A=∫abf1(x)-f2(x)dx