To find the point on a given curve at which the slope of tangent to the curve is a mimimum
For 6 points, solve ONE of the following three problems. Optimization Find the point(s) on the...
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Optimization problems 1. (5 points) Find two nonnegative numbers whose sum is 25 and so that the product of one number and the square of the other number is a maximum. 2. (5 points) Build a rectangular pen with two parallel partitions using 300 feet of fencing. What dimensions will maximize the total area of the pen? (5 points) An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions...
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3) Consider the function, f(x ) = sin x from x =-π to x = π. What is the slope of the line that passes through the highest point on the curve and the lowest point on the curve? 4) Given g(x)- 5) What is the area enclosed by the lines x = 4, y = 2, and xy = 24? Į sin (x...
MATLAB Assignment #1: Solve the following problems by writing commands in by writing a program in a script file and executing the file. Tum in a printout of the results and email the m file. All work should be individual, not shared 9. Let a 13, b= 4.2 (4b) abc d= ab+c then evaluate da - (a- )(c+ d) cb c+ d 10. A cube has a side of 18 cm. Detemine the radius of a sphere that has the...
Find the tangent line to the curve x-y = 6ey at the point (6,0). 6 (s 1+6e0 016e
Find the tangent line to the curve x-y = 6ey at the point (6,0). 6 (s 1+6e0 016e
Find the slope of the curve below at the given points. Sketch the curve along with its tangent lines at these points. r= - 4+4 cos 0; O= The slope at the point o = 5 is (Simplify your answer.) The slope at the point 0 = (Simplify your answer.) is Identify the curve r= - 4 + 4 cos 0. OA. OB. OC. Give a geometric description of the set of points in space whose coordinates satisfy the given...
number three please!
In each of Problems 1 through 6, find the mass and center of mass of the shell Σ 1. Σ is a triangle with vertices (1,0,0),(0.3.0) and (0, 0, 2), with 8(x. y. z)-xz+1. 2. Σ is the part of the sphere x2 +y2 +z-9 above the plane z= 1, and the density function is constant. 3. Σ is the cone z-yx't y,2 for x2 +y? < 9, δ constant
In each of Problems 1 through 6,...
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
can
you answer two of the questions in the phot please.
1. The point P(4. 8) lies on the curve y-(6-x), Suppose Q is the point (x,1 + (6-x)'). a. Find the slope of the secant line PO for the following values of x. 3. 3.99 4. 3.999 6. 4.1 7. 4.01 8. 4.001 the curve at P b. Use your results from part a to make a guess of the slope of the line tangent to c. Use your...
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find the maximum and the minimum of f(x, y) -yz on the sphere centered at the origin and of radius 3 in R3
Problem 5. Find saddle points of f(x,y)y sin(a/3). 82+88y6 a local Problem 6. At what point is the function f(x, y) minimum? Problem 7. Use Lagrange multipliers to find...
Each of these problems (Problems 1-4) is worth four points Definition: Two lines or curves are said to be normal to each other at their point of intersection if they intersect there at right angles or, equivalently, if their tangent lines at the point of intersection are 1. A well-known theorem in geometry states that a line which is tangent to a circle is perpendicular to the radius of the circle at the point of tangency. Use implicit differentiation to...