ignore the top part of graph Which of the following plots best represents level curves (with c=-1, 0, 0.5, 1, 2, and 4) of thefunction f?!!210.5-10,6A)B)-2-10-2-120:5-2C)D)-21-212 What is the best description of point (0,0) on the plot C) above?(i) Local minimum(ii) Local maximum(iii) Saddle point(iv) Critical point but neither maximum, nor minimum, nor saddle point

Answered: What is the best description of point…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

ignore the top part of graph

Which of the following plots best represents level curves (with c=-1, 0, 0.5, 1, 2, and 4) of the
function f?
!!
2
1
0.5
-1
0,6
A)
B)
-2
-1
0
-2
-1
2
0:5
-2
C)
D)
-2
1
-2
1
2

What is the best description of point (0,0) on the plot C) above?
(i) Local minimum
(ii) Local maximum
(iii) Saddle point
(iv) Critical point but neither maximum, nor minimum, nor saddle point

Expert Solution

Step 1

$A t p o i n t (0, 0) A s w e m o v e i n + v e x - d i r e c t i o n, f r o m x = (- 2, 2) a n d k e e p i n g y = 0 . F o r x (- 2, 0) : f (x, 0) d e c r e a s e s f r o m 4 t o 1 : f_{x}' (x, 0) < 0 A t x = 0 : f (x, 0) = 1 : f_{x}' (x, 0) = 0 (m i n i m u m v a l u e) F o r x (0, 2) : f (x, 0) i n c r e a s e s f r o m 1 t o 4 : f_{x}' (x, 0) > 0 A s f_{x}' (x, 0) g o e s f r o m - v e t o 0 t o + v e w i t h i n c r e a s e i n x h e n c e, f_{x}'' (x, 0) > 0 . H e n c e f (x, 0) i s c o n c a v e u p w a r d a l o n g + v e x - a x i s .$

Step 2

$A t p o i n t (0, 0) A s w e m o v e i n + v e y - d i r e c t i o n, f r o m y = (- 2, 2) a n d k e e p i n g x = 0 . F o r y (- 2, 0) : f (0, y) i n c r e a s e s f r o m - 1 t o 1 : f_{y}' (0, y) > 0 A t y = 0 : f (0, y) = 1 : f_{y}' (0, y) = 0 (m a x i m u m v a l u e) F o r y (0, 2) : f (0, y) d e c r e a s e s f r o m 1 t o - 1 : f_{y}' (0, y) < 0 A s f_{y}' (0, y) g o e s f r o m + v e t o 0 t o - v e w i t h i n c r e a s e i n y h e n c e, f_{y}'' (0, y) < 0 . H e n c e f (0, y) i s c o n c a v e d o w n w a r d a l o n g + v e y - a x i s .$

Step by step

Solved in 3 steps

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions