By using the definition of the derivative function (fJ(x) = lim f (x + h) − f (x)),

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. (2 points) By using the definition of the derivative function (fJ(x) = lim f (x + h) − f (x)), find the derivative of f (x) =2.3 − 5xh→0 h

2. (2 points) By using the definition of the derivative at a point a (fJ(a) = lim f (x) − f (a)), x→a x − a

compute the derivative of the greatest integer function f (x) = [x] at a = 3/2. Show that this function fails to be differentiable at the point a = 1. (3x2 + 4x if x ≤ 1 is continuous and differentiable at x = 1.

4. (2 points) Compute the derivative fJ(x) of the function f (x) = cos x + 2ex 7x3 and find fJ(π).

5. (2 points) Find the equation of the tangent line (in slope intercept form) to the curve

y = ex − sin x at the point (0, 1).

6. (Bonus, 2 points) Let f (x) =ax2 + bx + c if 0 < x 1 .3 − 2x if x> 1

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme