Use the First Derivative Test to find the location of all local extrema for the function given below. Enter an exact answer. If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter in the appropriate box. 20x3 f(x) = -x² + 3 Provide your answer below: +1

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: Find the area of the region enclosed by the inner loop of the curve. r = 2 + 4 sin ?

A:

Q: Consider the following revenue function, where ? is measured in dollars. R(x)=110x-0.1x^2 a. Use…

A: Consider the following revenue function, where R(x) is measured in dollars. R(x)=110x-0.1x^2 a. Use…

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: 4) A degree 3 polynomial function, P(x) has zeros x 2, x = 1, x = m and a leading coefficient of 1.…

A: Here, the polynomial P(x) is of degree 3 and has three zeros x=2,1 & m and the leading…

Q: Calculate[r₁(t) r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt the product directly and then…

A: r1=9ti+3t2j+8t3kr2=t4k

Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

A:

Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

A:

Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: Find the exact length of the polar curve. r = e4?,    0 ≤ ? ≤ 2?

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Q: Evaluate (1 + i)(¹ - i). (1

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Q: 3. An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a…

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Q: Find the area of the region enclosed by one loop of the curve. r = 7 cos4e Select the correct…

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Q: Find the sum of the first 125 positive even whole numbers.

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Q: Find the first four terms of the binomial series for the given function. (1+5x)1/2 5 125 25 OA. 1-x+…

A: We can find the first four terms as below.

Q: 5. Evaluate the integral, if it exists. a. L₂(x¹ - 3x¹/3 + 1) dx b. √₁³ (2ex - ²) dx

A:

Q: Solve the system using Cramer's Rule. - 6x + 6y3z = 15 x - 2y + z = 7 4x5y4z = - 28 Find the…

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Q: x³+2x-1 (x²+9)² The partial fraction decomposition of has the form None of these Ax+B (x²+9)² A x²+9…

A:

Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: Explanation of the answer is as follows

Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: A radar, using the polar coordinate system, detects that two airplanes are currently located at…

A:

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: As per bartleby guidelines we only give first three question answers.

Q: 22. Differentiate. y = asinh x

A: Given,  y=xsinh x

Q: Find the Laplace transform of sint 0<t<27 f() =

A:

Q: 109. ff(x)=x4 tan x³ -x In (1+x²), then the value of (b) 1 (c) da f(x) dx4 at x = 0, is: (d) 1 15

A: Use the properties of add and even function.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- Find the domain of r(t) and the value of r(t0)  r(t) = cos(πt)i - ln(t)j + √(t -…

Q: An open box of maximum volume is to be made from a square piece of material, s- 12 inches on a side,…

A:

Q: x2 – 3x – 2 if x 4 f (x) = - (2x + 1

A:

Q: 44. Find f(x) if f(x) = 1/(2 - x).

A:

Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given

Q: Solve [2*+2³ = 10 4* +4 = 68

A:

Q: Find the four second-order partial derivatives for f(x, y) = 8x5y³ +5x6y7.

A:

Q: Find the equation of the final function after all the following transformations have been made on y…

A: The below image has all the steps

Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

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Q: A local event center hosts wedding receptions The event center charges a rental charge plus a charge…

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Q: 2 Find the centroid of the portion of the sphere x² + y² + z² = 2a² that lies in the first octant.…

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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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Q: 3. Evaluate yn x dx

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Q: A company selling baseball gloves has fixed costs of $1800, and it costs an additional $23.71 to…

A: This question is related to Cost and Revenue function, we will solve it using given information.

Q: A 17 cm x 11 cm open rectangular box is to be constructed by cutting square corners out of a piece…

A: Let the sides of square be x cm then the dimensions of the box will be as follows Dimensions of box…

Q: PART I: Write an expression that is complex enough to be differentiated using the: Product Rule…

A:

Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…

Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: ZzJm 3. Use integral test to determine whether the series 4. Use an appropriate test to determine…

A: 3. ∑n=1∞e-n2n4. ∑n=1∞n2n+1!n! 22n

Q: 6. A parallelogram is defined by the vectors (4, 3) and (1, 2). Determine the perimeter of the…

A: The parallelogram is defined by the vectors (4,3) and (1,2)  We have to determine the perimeter of…

Q: Use the appropriate technique of integration to compute the following antiderivatives. SHOW THE…

A: Solve the following

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: Consider the polar curves Cı :r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

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Q: Problem 3. Solve 2+2 =10 4* +4 = 68

A: To solve the following system of equations.2x+2y=104x+4y=68