Domain, Range, and Level CurvesIn Exercises 1-4, find the specific function values.1. f(x, y) = x² + xy%3Dа. f(0, 0)b. f(-1, 1)с. f(2, 3)d. f(-3, –2)2. f(x, y) = sin (xy)- (2=)TTа.b.a. 1(-3-1)с.х — у3. f(x, y, z) =y² + zа. f(3, —1, 2)b.d. f(2, 2, 100)с.4. f(x, y, z) = V49 – x² – y² – z?%3Dа. f(0, 0, 0)b. f(2, –3, 6)456с. f(-1, 2, 3)d.Please do question 3.

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Answered: х — у 3. fx, y, г) y? + z? а. f(3, —1,…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 48CR

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Нomеwork: 1. Find the max., min., inflection points and the intervals on which the functions increase, decrease, concave up and concave down. (a) y= 4x+6x² -6x-4 (b) y= x' -8 (d) y=(x- 2)3 2/5 (c) y=3x+(x-2)²5 2. Find the intervals on which f are: (i) Increasing and decreasing. (ii) Concave up and concave down. and the x-coordinate of all critical and inflection points. (a) y=x -5x+6 (b) y=(x+1)³ (c) y=x* -8x² +16 (d) y= 3x - 4x (e) y = () y = x+2 x² +2 1/3 (h) y = x" (x+2) *9 -x 4/3 (8) y=Vx+2 (i) y =x (G) y= cos x; [0,27] (k) y= sin² 2x ; [0,7) (1) y=2x+cot x; [0,7] (m) y= sin xcos x; [0,7]
A. Matching Type. Match the functions in Column A with their corresponding derivatives in Column B. Column A Column B А. F(x) %3D 2х3 — 2x2 + х В. F(x) 3D х3 + 3x2 + х а. f(x) 3 4x3 + 3x2 b. f(x) 3 Зx2 + 3 с. f (x) %3D Зx2 + 6х + 1 d. f(x) — 6x2 —- 4х + 1 е. f(x) 3D 8x3— 9х2 С. F(x) 3D 2x4 - 3x3 + 1 D. F(x) 3 x4 + х3 — 5 Е. F(x) 3 х3 + Зх + 1
Find the directions of maximum and minimum change of f at the given point, and the values of the maximum and minimum rates of change. f{x, y) = 4y²e*, (2, –4) The maximum change is 32e V37 ; in the direction (-192e“, 32e®); The minimum change is –32e V37 ; in the direction (192e", -32e). The maximum change is 32e6 The minimum change is –32e 6 V37 :; in the direction (192e, -32e ). V37 ; in the direction (-192e6, 32e ); The maximum change is 32e V37 ; in the direction (192e, -32e); The minimum change is –32e V37 ; in the direction (-192e", 32e). The maximum change is 32e V37 ; in the direction (192e ,–32e ); The minimum change is –32e 6 V37 :; in the direction (-192e, 32e ).
Differentiate. 4) f(x) = e2x 5) y = e6x2, x
(a) Find the slope m of the tangent to the cûrve y = 7//x at the point where x = a > 0. %3D m 41 (b) Find equations of the tangent lines at the points (1, 7) and y(x)%3D (at the point (1, 7)) Y(x)%3D at the point (4, 3) (c) Graph the curve and both tangents on a common screen. у 15 10 -4 -2
V6 5 V6 5 Select an appropriate graph of a twice-differentiable function y=f(x) that passes through the points (-V2,1),| -- .(0,0), 3 '9 3 '9 and (V2 ,1), and whose first two derivatives have the following sign patterns. 12 V6 V6 3 3 OA. ов. Oc. OD. Ay 18 54 Ay 18- -3 3 -18
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х — у 3. fx, y, г) y? + z? а. f(3, —1, 2) b. с. d. f(2, 2, 100)