diff quotient-6

# diff quotient-6 - THE DIFFERENCE QUOTIENT I The ability to...

This preview shows pages 1–2. Sign up to view the full content.

THE DIFFERENCE QUOTIENT I. The ability to set up and simplify difference quotients is essential for calculus students. It is from the difference quotient that the elementary formulas for derivatives are developed. II. Setting up a difference quotient for a given function requires an understanding of function notation. III. Given the function: f(x) = 2 3x 4x 5 A. This notation is read “f of x equals . . .”. B. The implication is that the value of the function (the y-value) depends upon the replacement for “x”. C. If a number is substituted for “x”, a numerical value for the function is found. D. If a non-numerical quantity is substituted for “x”, an expression is found rather than a numerical value. E. Careful use of parentheses is essential! IV. Examples using f(x) = 2 3x 4x 5 A. 2 f(4) 3(4) 4(4) 5 27 = = B. 2 f( 3) 3( 3) 4( 3) 5 34 = = C. f(a) = 2 3a 4a 5 D. 2 f(2a 3) 3(2a 3) 4(2a 3) 5 = 2 3(4a 12a 9) 8a 12 5 = + + = 2 2 12a 36a 27 8a 12 5 12a 44a 34 + + = + E. = 2 f(x h) 3(x h) 4(x h) 5 + = + + 2 2 3(x 2xh h ) 4x 4h 5 + + 2 2 3x 6xh 3h 4x 4h 5 = + + F. = 2 f(5 h) 3(5 h) 4(5 h) 5 + = +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern