Use the product rule to find the derivative of the given function. Hint: Write the quantity as a product. y= (7x³+3x²)² y' = ☐

Q: Consider the function f(x)=2x^3-12x^2-30x+2 on the interval [-6,10]. Find the average or mean slope…

A: The answer is given below.Explanation:

Q: Given that h'(x) = 4x² - 2x 2x and h(1) = 2, find h(x).

A:

Q: Sketch the graph of a function g with the property that g'(x) 0 for x> -3. Choose the correct graph…

A: To choose the graph of a function  with the property that .

Q: V) For the following exercises, use the given information about the polynomial graph to write the…

A: solution 1polynomial  f(x)=3−2​(x+2)(x−1)(x−3)solution 2polynomial…

Q: A stone is thrown straight down from the edge of a roof, 1150 feet above the ground, at a speed of 5…

A:

Q: Show all proper work this is the curve sketching unit in calculus Both a,b,c are part of 1 question

A: Step 1: Step 2: Step 3:

Q: A 500-gallon tank contains liquid that is 10% alcohol (the tank is full). A 50% alcohol liquid…

A: Step 1: Step 2: Step 3: Step 4:

Q: Use Newton's method to estimate the one real solution of x3+4x-1=0. Start with x=0 and then find X2-…

A: By using Newton's method to find  by starting with for thefollowing equation.

Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (6,…

A:

Q: How does y= sin x compare to y= cos x in terms of transformation (explain) convert • f(x) = Cos…

A: 1. To understand how y = sin x compares to y = cos x in terms of transformation, we need to analyze…

Q: Let f(x) = 3x2+5x-10. Answer the following questions. 1. Find the average slope of the function f on…

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

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Q: Solve and show all steps

A: I hoe this helps you! Thank you!  If there's any doubt please comment down i will surely be there to…

Q: R 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9 ≤ x² + y² ≤ 25 by…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over a…

Q: Consider the function f(x)=10 root x +10 on the interval [2,5]. Find the average or mean slope of…

A: Therefore, the required answers are a) The average slope is m=310​(5​−2​)=2.739514717088982158b)…

Q: f'(0) = Let f(x)=7e+2 + e¹.

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Q: d11 is not a grade is a standard!!

A: Step 1:Part(a)(i) Yes, the graph indicates that x=0 is a critical point.A critical point of a…

Q: x-17 Find the area bounded by y = x²-3x-54 (Round the answer to four decimal places.) , x = 2, x =…

A: The area bounded by the curve y=x3−3x−54x−17​ is approximately 0.7868.Explanation:Evaluate the…

Q: Sketch the region in the first quadrant enclosed by y = 7/x, y = 2x, and y = x. Decide whether to…

A:

Q: Consider the function f(x)=1/x on the interval [1,11]. Find the average or mean slope of the…

A: The objective of this question is to find the average slope of the function f(x)=1/x on the interval…

Q: Find the volume of the solid between the following surfaces. Show all the steps

A: using cylindrical shell method volume=27π​  cubic unit Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Find the linear approximation to the following function at the given point a. f(x)=3x-1; a= -2 L(x)=…

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Q: -√x [3] (a) Evaluate dx √x (b) Determine if the following integrals are convergent or divergent.…

A: (a) To evaluate (b) To determine whether the following integrals are convergent or divergent.To…

Q: You borrow $300,000.00 that charges you 5.1% interest, compounded monthly. You will make payments…

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Q: Find the smallest perimeter and the dimensions for a rectangle with an area of 25 in² The smallest…

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Q: (1) Evaluate the iterated integral by converting to polar coordinates. 2√2x-x2 x² + y² dy dx

A: A given integral We have to integrate it by converting it in polar coordinates

Q: Kasia plants her watermelons in rows. Kasia's watermelon field has a perimeter of 71(1)/(3) yards…

A: The perimeter of the Kasia's watermelon field is :

Q: 2. Area of a circle: Consider the polar equation r = 2Rsine. Sketch the graph and note the limits…

A:

Q: 14

A: To find the volume formed by rotating the region enclosed by the curves y=4x​​ and y=x about the…

Q: I)For the following exercises, determine the least possible degree of the polynomial function shown.…

A: 1) 32) 23) 5Explanation:A polynomial of degree n has at most (n-1) turns.Thus, the least possible…

Q: Let f(x) = 3x² - 2x. (a) Use the definition of derivative and the Procedure/Example box in this…

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Q: Find the indefinite integral and check the results by differentiation

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Q: 3 1 -2 3 A = B = 02 -1 10 -20 4 -1] -22 calculate (if possible): a)-3AT+2B Instructions for the…

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Q: Find the slope of the tangent line for the curve r = -7-7 cos 0 when 8 = 2

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Q: 8

A: using washer method Volume=43π​  cubic unit Explanation:Step 1:Step 2: Step 3: Step 4:

Q: 7π Convert the point (p, 0, 0): 6. to Cartesian coordinates. Give answers either as expressions, 6 3…

A: The objective of the question is to convert a point from spherical coordinates to Cartesian…

Q: List the points in the graph in the interval -1 <x<7 at which the function is not differentiable.

A: If a function is not continuous at x=a, then it is not differentiable at x=a.

Q: Find the curvature of the curve (t) = = (3 cos(2t), 3 sin(2t), 3t) at the point t = 0 Give your…

A:

Q: Homework

A: −63.22​Explanation:ANSWER : ​​

Q: 4  For the function shown in the​ graph, give the​ interval(s) where the rate of change of​ f(x)…

A: Step 1:a) The rate of change is positive on the interval where the slope is increasing. From the…

Q: A baseball team plays in a stadium that holds 46000 spectators. With the ticket price at $10 the…

A: Given points: (10, 19000) and (9, 23000)Calculate slope m: (23000−19000)​/9-10=−4000Use slope m and…

Q: ☐ 4. What is step 1 for calculating volumes by shells? See where that x or y hits any curves, and…

A: The correct step 1 for calculating volumes by shells is:d) Pick a rectangular piece that is parallel…

Q: 1 5. Given: cot(x)= π and 0<x<, find the value of the following expression using sum 20 and…

A:

Q: Given cos(x) 84 O 85 13 O 85 77 85 126 85 36 85 35 15 with 0° << 90° and cos(y) with 270° < y < 360°…

A: 8577​ Explanation: Given that, cosx=53​    with   0∘&lt;x&lt;90∘  cosy=1715​     with…

Q: Ay 15 12 9 Solve graphically by the intersection method. Give the solution in interval notation.…

A: The objective of this question is to find the point of intersection of the two given lines y₁ =7x+…

Q: Sketch the graph of a function g with the property that g'(x) 0 for x > -3. Choose the correct…

A: The objective of the question is to identify the correct graph of a function g based on the…

Q: Suppose f" (x) > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: The objective of the question is to determine which of the given statements are true given that the…

Q: 11. A snowball melts so that its radius decreases by 0.2 cm/min. Find the rate at which the surface…

A: A snowball melts so that its radius decreases by 0.2 cm/min. To find the rate at which the surface…

Q: The gradient function of a curve is f'(x) = 2kx +7. Given that f(0) = 6 and f(2) = 8, find the value…

A: The gradient of the function is given byThe initial conditions areTo determine: The value of .

Q: The function f(x)=2x^3-27x^2+48x+8 has one local minimum and one local maximum. Use a graph of the…

A: Answer ....This function has a local minimum at x = 8 with output value  f(x)= -312and a local…