please answer question 1 ans 2 ### Problem 2: Sketch the Graph of a Continuous Function \( f \)1. The conditions for the function \( f \) are as follows: - \( f(2) = 1 \) - \( f'(2) = 0 \), meaning the point \( (2, 1) \) is a local minimum of \( f \).2. Further conditions: - \( f \) is undefined at \( x = 3 \). - The first derivative \( f'(x) < 0 \) on \( (-\infty, 3) \cup (3, \infty) \). - The second derivative \( f''(x) < 0 \) on \( (-\infty, 3) \). - The second derivative \( f''(x) > 0 \) on \( (3, \infty) \).### Explanation:This problem asks us to sketch the graph of a continuous function \( f \) given specific conditions concerning its values, derivatives, and points of discontinuity.#### Detailed Conditions:1. **For \( x = 2 \):** - The function passes through the point \( (2,1) \), i.e., \( f(2) = 1 \). - The function has a zero slope at \( x = 2 \), \( f'(2) = 0 \), meaning it is a critical point. - The point \( (2, 1) \) is a local minimum.2. **Around \( x = 3 \):** - The function is not defined at \( x = 3 \). - \( f'(x) \) is negative to the left and right of \( x = 3 \), implying the function is decreasing on these intervals. - The concavity of the function changes around \( x = 3 \) as indicated by \( f''(x) \): - \( f''(x) < 0 \) on \( (-\infty, 3) \), indicating concave down (i.e., the graph bends downwards). - \( f''(x) > 0 \) on \( (3, \infty) \), indicating concave up (i.e., the graph bends upwards).These conditions will help in sketching the graph precisely, noting the abrupt change in behavior at

We have to sketch the graph for given question.

•. Sketch the graph of a continous function & f(2)=1 f'(2)=0, the point (2,1) is 1 1 1 1 2 I is undefined at x=3 e) <0 on (-0,3) ~ (3,00) + " (*) <0 on (-∞, 3). {"(x) > 0 on (3, 0) so that a local minimum of

•. Sketch the graph of a continous function & f(2)=1 f'(2)=0, the point (2,1) is 1 1 1 1 2 I is undefined at x=3 e) <0 on (-0,3) ~ (3,00) + " (*) <0 on (-∞, 3). {"(x) > 0 on (3, 0) so that a local minimum of

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

Similar questions

to 20
number of economy passengers is incorrect
1. x? + 4 mLA = mLB = mLC = mLD = 5x + 40 D
Number 22 please
,2 3 FルD
6+5.2-4=
Help
do 7 please
Firel for