TYPEWRITTEN ONLY PLEASE FOR UPVOTE. DOWNVOTE FOR HANDWRITTEN. DO NOT ANSWER IF YOU ALREADY ANSWERED THIS 4.) Consider the functiong defined byga, y) - cos (T x Jū ) +X.logg(x-y)(c) in what dire ctiondoeshave the maximumdirectionalderivative at ,y) - (4,1)?What is the maximum directional derivative ?

Given function = g(x,y)=cosπxy+1log3x-y point= (4, 1) To find: What is the maximum directional…

Answered: Consider the function g defined by gx,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Find the derivative of each function a) f(x) = x³e/x et3+7 b) g(t) = t2 c)유x2 n( 2x + 1) 8x+9.
Find the derivative if the following and simply to its simplest form: a) y= (4t² – 3t + 2)-2 (x+3)4 b) y= Vx2+5 c) f(x)= x³(4x – 1)² .3
Assume that functions f and g are differentiable with f(4)= -2, f'(4) = 3, g(4)=-4, and g'(4)= -2. Find an equation of the line tangent to the graph of F(x) = f(x)g(x) at x = 4. The equation of the tangent line is (Type an equation using x and y as the variables.) this Get more help - er.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandles Locale=true# Will H a J i O prt sc F10 home F11 Clear all end F12 insert Check ans 10/ delete
Calculate the second and the third derivative of y = 3x y" = y'" = Note: You can earn partial credit on this problem. 1 inflection points 3 X blem 10. Find the inflection points of f(x) = 6x4 +58x³ - 30x² + 10. (Give your answers as a comma separated list, e.g., 3,-2.)
17. Sketch the ioiicwing curve by cing seconá derivative: 1) y= 1+x 2) y=-x(x-7) 3) y (x+ 2) (x-3) 4) y=x(5-x) (ans.: max.(1,0.5); min.(-1,-0.5)) (ans.: max.(7,0); min.(2.3,-50.8)) (ans.: max.(-2,0); min.(1.3,-18.5)) (uns. mux.(3.5,18.5);ra0,0)) 18. What is the smallest perimeter possible for a rectangle of area 16 in.2 ? (ans.: 16) 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the parabola y 12-x. (ans.:32) 20) A rectangular plot is to be bounded on one side by a straight river and enclosed on the other three sides by a fence. With 800 m. of fence at your disposal. What is the largest area you can enclose ? (ans.:80000) 21) Show that the rectangle that has maximum area for a given perimeter is a square. 22) A wire of length L is available for makıng a circie and a square. How should the wire be divided between the two shapes to maximize the sum of the enclosed areas? (ans.: all bent into a circle) 23) A closed container is made from a…
6. Let y + xy -y = 8x*. a) Find d/dx using implicit differentiation. b) Find the equation of the tangent line to the graph of y3 + xy- y = 8x* at x = 1.
Consider the function f(z) = (x – 1)e". a) When is f(r) = 0, when is f(x) > 0 and when is f(r) < 0? b) Compute the derivative of f. Find all stationary points, and describe when the function f is increasing and when it is decreasing. c) Compute the second derivative of f. Find all inflections points, and when the function f is concave, and when it is convex. d) Provide a sketch of the function, where you include all the important infor- mation that you have computed in point a)-c). (Here you can also write the important information besides the graph if you want).
1. Determine whether the given functions are differentiable (anywhere). If the function is differentiable then find its' derivative. i) f(2)=-2(xy + x)+i(x²-2y-y²) ii) 8(z)-2+z iii) f(z)-e² (cos(²-x)+sin(x²-x²)) 2. Find the square root of -5+5 3. f(2)=2³ +42-6 in the polar coordinate form u(r,0) +iv(r,8).

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Consider the function g defined by gx, y) • car (7x Jy ) + r (I X Jj ) + cos logg(x-y)