Question: Is the following true or false? (a) If a function f is continuous at x = 0, then the derivative, f'(0) exists. (b) If f

Is the following true or false?

(a) If a function f is continuous at x = 0, then the derivative, f'(0) exists. (b) If f is differentiable at 2: =11, then f must be continuous at x = a. (c) If the tangent line to the graph of f at the point (a, f ((1)) has equation 2x +y+ 3 = 0,thenf'(a) = 2

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

(1) Consider the following system of linear equations - by - 2: = I - 03 b r+ (2 -b)y where a, be R. (a) Classify the system according to the values of a and b. (b) Solve the above system for the...

Hi, I have real analysis questions. I need your help. Thanks a lot. 3) Let f(x) = sin(1/x) for x E (0, oo). Define f(0) to be any real number of your choosing. Argue that Jon f exists, and it is...

Please solve and explain this question in details. 5d and 6c but i don't know why. 5. Consider the graph of the derivative of the function y = f(;1;) given below. 14 = f'() Which of the following...

Determine if the following statements are true or false. a. If a function f has an absolute maximum on the interval [1,3] , then it also has an absolute minimum on the same interval. True False b. If...

erentiability f' (x) = lim (ath) f(x) itf (x) = . Use the definition of the derivative to determine if the function is differentiable at x = h-0 o f (x) is not differentiable at x = 0 because the...

Hello, I have a real analysis question. I need your help. Thank you so much. 6) Where is the function f differentiable? And compute the derivative where it exists. f (2 ) = x sin x = 0 Where is the...

Answer the following True or False If f x is a differentiable function at x 4 then f x is continuous at x 4 True False

1. (6 points) Given the differentiable functions f(x) and g(x), and their derivatives in the table below, find the value of the following limit. Answers without supporting work will not receive...

1. (30%) True and False (1) If a function f can be expressed as fag*h, a multiplication of 2 functions, g and h, then D(f)=D(g*h)= h*D(g) +g"D(h) is always true. (2) If f is continuous over (a, b),...

\f5 -3- -3 -2 0 2 3 5 10 -1- A. f(x) is discontinuous at x = 2 because lim f(x) # lim f(x) x-2 x -+ 2+The attached image is a graph of the function f(x). Which of the following statements is false?...

Sato Jewellers has had a request for a special order for 10 gold bangles for the members of a wedding party. The normal selling price of a gold bangle is $389.95 and its unit product cost is $264.00,...

During the Spring 2009 semester at Monroe Community College, a random sample of students was questioned on their knowledge of the meaning of sustainability. The primary motivation for the survey was...

Calculate the accumulated amount to 2 decimal places at the end of year 1 7 of the following regular series of payments made into a savings plan: 1 9 1 7 per annum paid monthly in advance in years 2...

The data set labeled Cola Weights and Volumes includes volumes (ounces) of a random sample of 36 cans of regular coke in the column labeled COKE REG VOL. Use a 0.05 significance level to test the...

5. How can a sender (utterer) directly influence the interpreter (receiver)?

10. Find a news article in a daily newspaper, and answer the following questions: (a) Does the information in the article support your views and attitudes or does it conflict with them? (b) Does the...

2. Give an example where information that is emotionally interesting, specific and close in time and space, can be used to capture someones interest.