For the function f(x)-4+ 12x²-x³, find the local extrema. Then, classify the local extrema using the second derivative test.

Q: > #11 Given z = f(x,y) = 3xy , у find the equation of the tangent plane to the graph, when x=1, y=3.

A: Equation of tangent is z=4x−34​y−2Explanation:

Q: I have a set of vectors in R^2(i.e. two-dimensional vectors) such that the scalarproduct (the same…

A: The maximum number of vectors in your set in R², where the scalar product of any two vectors is…

Q: Suppose z x2 sin y, x = 3s² + 312, y = 2st. =

A:

Q: Find the arc length of the curve on the given interval. x²,y=141, 0 ≤t≤7 Select one: O a.…

A: Given the parameteric form of a curve.

Q: X+2 At what points is the function y = continuous? x²-11x+18 Describe the set of x-values where the…

A: Given function is We have to find the points where the given function y is continuous.

Q: Calculus I May I please have the solution for the following questions? Sketch an accurate graph…

A: Please refer below to get your solutions.Explanation:Sol -> a) Sol -> b) Sol -> c) Sol…

Q: 1. Given the differential equation below, find the solution using Laplace transformation. The…

A: The objective of this question is to solve the given differential equation using Laplace…

Q: 6. Sketch an even continuous function with all of the following features: • Absolute minimum at -5 •…

A: Function is even continuous  function.  Absolute minimal at -5 Zeroes at 4 and -4y- intercept at -23…

Q: 10 m₁-m 2 = 5 m₁+ m2 1 Solve for m₁

A:

Q: (c) [6 pts] In(x + 1) In(1 - x) = 2. I (d) [7 pts] 2.31-2x = 7.64+x

A: Question cx = 0 and 3 Question dx=−3ln(3)+ln(2)3ln(2)+3ln(3)+ln(7)​≈−1.835Another way of expressing…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Given that when air expands adiabatically (without gaining or losing heat), its pressure P and…

Q: Use the linear approximation of f(x, y) = 3x+2y at (0,0) to estimat f(-0.02, 0.03)≈

A:

Q: Evaluate the following integrals using partial fraction decomposition, when applicable. 16. dx…

A: 16). I=51​ln∣x+1x−4​∣+C 17).  I=2−3​ln∣2x+1∣+2ln∣x+2∣+CExplanation:Step 1: Step 2: Step 3: Step 4:

Q: 2 #12 Given f(x, y, z) = 3√ √ x²+ y²+z² (a) Find the linear approximation L(x, y, z) near the point…

A: a.) The linear approximation is L(x, y, z) = 2√2 + (-1/√2)(x + 2) + (1/√2)(z - 2)b.) The linear…

Q: Evaluate the following integrals using partial fraction decomposition, when applicable

A: Answer ∫(2x−3)(x2+1)13​dx=2ln(∣2x−3∣)−ln(x2+1)−3tan−1(x)+C…

Q: The graph of a function is given. Choose the answer that represents the graph of its derivative…

A: We need to determine the graph of the derivative from the given graph.

Q: Now, we can find the revenue function by multiplying the price function by the quantity function and…

A: Revenue function can be obtained by multiplying the price function by the quantity function.

Q: Use Linear Approximation to estimate Af = f (9.02) - f(9) for f(x) = x4. (Use decimal notation. Give…

A:

Q: C(q)=560+ 15g, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars…

A:

Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A:

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 32+ y² = 5. maximum value =…

A:

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

A: The given revenue function

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The exact area of the parallelogram is 726​. The approximate area of the parallelogram is…

Q: Find all points (if any) of horizontal and vertical tangency to the curve x = 6+2cose, y = -2+ sine.…

A:

Q: dy dx = dy 33 dx = y = ln 3x14 +1 y = x cos(x)

A: The solution and explanation of the given problem are attached below.Explanation:Step 1:

Q: What are the absolute max and min values for the following function: f(x,y) = x3+x2y+2y2 on the…

A: Answer:Absolute maximum value of function = 2Absolutely minimum value of function = 0The detailed…

Q: Match the following log expressions to their correct evaluation. 1. 5 1+In(e²)-3log2(4) In(e³) 2. 4…

A:

Q: f(x, y, z) = xe²yz, P(1, 0, 1), u = (a) Find the gradient of f. Vf(x, y, z) = < (b) Evaluate the…

A: Therefore, the required answers are a) "&gt;▽f(x,y,z)=&lt;e2yz,2xze2yz,2xye2yz&gt;b)…

Q: Solve the following logarithm equation then input your solution as an integer in the blank provided…

A: The equation:

Q: The estimated resale value R (in dollars) of a company car after t years is given by R(t)=23,806…

A: The estimated resale value  of a company car after  years is given by .We have to find the rate of…

Q: f'(x) = ƒ' (e³) = f(x) = (ln x)7

A: ∙  f′(x)=x7(lnx)6​∙  f′(e3)=e35103​Explanation:

Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: Please see the explanation Explanation:Step 1:

Q: Problem #3: Consider the following function. f(x, y) = 2x3+24xy-12y2 (a) Find the critical points of…

A: Refer explanationExplanation:

Q: The sides of a square carpet is measured at 2 ft. Estimate using the Linear Approximation the…

A:

Q: Find f'(x). f(x)=5x-4ex

A: f′(x)=5exe−1−4exExplanation:

Q: 2. Consider the region S bounded by the curves 1 y=x+ and y=x- 14 a. x" for x≥1 Is the area of S…

A: The objective of this question is to determine whether the area of the region S bounded by the…

Q: (3 points) By setting one variable constant, find a plane that intersects the graph of z=3y29x2 +5…

A: (a)z=3y2+5(b)z=−9x2+5(c)z=5Explanation:Given the equation,z=3y2−9x2+5 This surface is a hyperbolic…

Q: The length {, width w, and height h of a box change with time. At a certain instant the dimensions…

A: Detailed solution of the problem is attached below,Feel free to comment below if you want any…

Q: Find the exact value of each expression. (a) sin 75° sin 5° = 0 (b) cos 105° - cos 15° = 0

A: Formulas are used for solving this problem:-

Q: Find all points (x,y) on the graph of f(x) = 2x² - 3x with tangent lines parallel to the line y =…

A:

Q: Match each of the trigonometric expressions below with the equivalent non-trigonometric function…

A: Correct matches are:A. 3 B. 1 C. 5 D. 4 E. 2Explanation:A.  tan⁡(arcsin⁡(x/3)) corresponds to option…

Q: Suppose the following is a sample of the day-by-day change, rounded to the nearest 100 points, in…

A: The objective of the question is to calculate the mean and median of the given sample of changes in…

Q: what's the final answer to a and b?

A: The objective of the question is to find the moment of time t0 and the point P0 on the curve r(t)…

Q: Write the corresponding rectangular equation for the curve represented by the parametric equation…

A:

Q: 29 Find the area under the curve y = from x = 1 to x = t. Evaluate the area under the curve for t =…

A:

Q: Approximate 1714 using the Linear Approximation L(x) of f(x) = x 1/4 at a = 16. (Use symbolic…

A: The given function The linear approaximation at

Q: All solutions of the differential equation  y' = −6 − y4  are decreasing functions.

A: The objective of the question is to determine whether all solutions of the given differential…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: √x(t) = −3+² -…

A: Therefore, the required answer is x=16−3​y2+89​y−1627​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Use the Chain Rule to find Əz/ǝs and Əz/ǝt. z = x5y5, x = s cost, y = s sin t Z Əz || дл at ||

A: Answer is given below.Explanation:Step 1:--Step 2: Step 3: Step 4:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: The required answer is 24Explanation:Step 1: Step 2: Step 3: Step 4: