Let f(z) =e (243z+4). %3D The derivative of f is f'(x)= e^(-2x^2-3x-4)(-4x-3) An equation for the tangent line to the curve y = f(z) at a = 1 is y = |
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A: It is derivative.
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A: We will find the first step of differntiation as following
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A: Note: As in questions d and e no instruction is given solved f and g for you.
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A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.
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A: The derivative is calculated as:
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A: Hi! Your question contains many sub-parts. As per norms we will be solving only 3 sub-parts. Since…
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Q: find derivative 1. y = ln (3ue^-u) 2. y = ln (2e-^t sin t) 3. y = e^sin t (ln t2 + 1)
A: find derivative
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- Ol’-Time Quilts receives an order for a patchwork quilt made from square patches of three types: solid green, solid blue, and floral. The quilt is to be 8 squares, and there must be 15 times as many solid squares as floral squares. If Ol’-Time charges $3 per solid square, $5 per floral square, and if the customer wishes to spend exactly $300, how many of each type of square may be used in the quilt? Give a general solution stating any limitation on the parameter. Then provide two specific solutions and compare. Is one of those two solutions preferable over the other? If so, why might be the case? If not, why are the two specific solution equally preferable?Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist, enter DNE.) g(x) = x2 + 5x + 4 Relative maximum (x,y) = relative minimum (x,y)= f(x) = x3 − 75x + 1 Relative maximum (x,y)= relative minimum (x,y)= f(x) = 3x4 − 4x3 + 6 Relative maximum (x,y)= Relative minimum (x,y)= Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x)= -0.003x2+6x-5,000 Increasing: Decreasing: Growth of Managed Srvices Almost half of companies let other firms manage some of their Web operations—a practice called Web hosting. Managed…University Calculus Early Transcendentals section 13.7 problem 28 finding all the local maxima, local minima, and saddle points of the function. F(x,y)=e^x(x^2-y^2). After finding (x^2-2x+y^2)e^x=0 and -2ye^x=0. How are they solved to find(x,y)=(0,0) and (-2,0)
- The function f(x,y)=e3xy has an absolute maximum value and absolute minimum value subject to the constraint x^2+xy+y^2=9. Use Lagrange multipliers to find these values. The absolute maximum is? (Type an exact answer in terms of e.) The absolute minimum is? (Type an exact answer in terms of e.)13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]Part 1.Find the dimensions of the rectangular box having the largest volume and surface area 24 square units. List the dimensions in ascending order ( , , ) Part 2.Locate all the critical points of the function f(x,y)=10x−x2−5xy2.
- 1. Find the monotone interval of y= (x-3)2/4(x-1) 2. Prove the inequality x>ln(1+x), where x > 0 3. find the intervals of convexity and concavity and inflection points Of the function f(x) = x4-2x3+1 4. the local extreme values of f(x)=(x2-1)3+1 5. Find global extreme value of f(x)=(2x -1).cube root of(x-3)2 on the interval [1/2, 4] 6. graph the f(x)=x3-x2-x+1 7. find the intervals of monotocity ,intervals of convexity and concavity , local extreme values and inflection point of f(x)=2x/1+x24. Zack consumes mangosteen(m) and chalta (c) and his satisfaction function from consumingthese fruits is given by S = (m+2)(y+1) The price of mangosteen Pm = 4 and the price of chalta, Pc = 6. He has 130 taka to spend on these fruits.a. Write the Lagrangian function.b. Find the optimal levels of purchase for mangosteen and chalta.c. Use bordered Hessian to prove that the second order condition is satisfied.d. What is the value of the Lagrangian multiplier? Show that if the budget is increased by one Taka,the increase in his satisfaction level is equal to the value of the Lagrangian multiplier.We know that x = 0 is the minimum. Show that x = -2 is the local maxima and with the Monotony criteria or another criteria one that there are not extrema
- This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = x2 − y2; x2 + y2 = 49 Maximum Value=? Minimum Value=? Thank YouSecant MethodIterative Formula:Xnew = x1 - [(f(x1) * (x1 – x0)) / (f(x1) – f(x0))]PROBLEM:f(x) = x3 + 5x2 + 7x – 20Use initial value of (1,2). Stop if you reach 5 iterations.COMPLETE THIS TABLE PLSA rectangle is constructed with its base on the diameter of a semicircle with radius 18 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area? Let A be the area of the rectangle. What is the objective function in terms of the base of the rectangle, x? The interval of interest of the objective function is? The rectangle with maximum area has base (enter your response here) and height (enter your response here)