how to simplify the difference quotient

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Question:Given the function f(x)=4-2x-x^2 Evaluate the difference quotient for the given function and simplify the answer. [f(1+h)-f(1)]\h I've tried to work this problem several times on an online homework website but it keeps saying my answer is incorrect, so I don't know what I'm doing wrong. Can someone help work this out for me?

Answers:f(1+h) = 4 - 2(1+h) - (1+h) = 4 - 2 - 2h - 1 - 2h - h = 4 - 2 - 1 - 2h - 2h - h = 1 - 4h - h f(1) = 4 - 2 - 1 = 1 f(1+h) - f(1) = -4h - h [f(1+h) - f(1)] / h = -(4h + h ) / h = -h(4+h) / h For h 0 we may cancel the factor of h from numerator and denominator, leaving [f(1+h) - f(1)] / h = -(4+h)

Question:The difference quotient is the basis of beginning to study a first Calculus course. Introductory Calculus is heavily based on Algebra. The difference quotient of a function f(x) is defined as f(x+h)-f(x) / h You can find the difference quotient in steps, if desired 1.Find the expression for f(x + h). 2.Find the expression for f(x + h) - f(x). 3.Find the expression for the difference quotient. 4.Simplify, if possible. Find the difference quotient for f(x)= (x+1)^3.

Answers:1. f(x+h) = ((x+h) + 1)^3 2. f(x+h) - f(x) = ((x+h) + 1)^3 -(x+1)^3 3. (f(x+h) - f(x))/h = (((x+h) + 1)^3 -(x+1)^3)/h 4. = (3x^2h +3xh^2 +6xh +3h +3h^2 +h^3)/h = 3x^2 +3xh +6x +3 +3h + h^2

Question:function is f (x) = 1/x. difference quotient is [ f (x) - f (a) ] / (x - a) Now I understand you merely use the first function and plug it in changing the x to an a with f(a). So I did that but I think when simplifying my algebra might have been a little off. If you could help I'd truly appreciate it.

Answers:We know that: f(x) = 1/x f(a) = 1/a Then: [f(x) - f(a)] / (x - a) = (1/x - 1/a) / (x - a) = (a - x) / [ax(x - a)] (multiply by xa/xa) = -(x - a) / [ax(x - a)] = -1/ax <== ANSWER I hope this helps!

Question:Find the difference quotient for the function f(x)=9x+8, and simplify it. I don't know. That's why I'm here and trying to figure this one out. I don't get it. Well, I'm at a community college right now. Maybe that's part of the problem?? This is an entirely new concept to me...I am an arts major and never have been mathematically/scientifically inclined - if there was a way both math & science could be better incorporated into 'everyday' situations (in my opinion they are not), then I think I could understand this stuff a little better! But that's just me. :)

Answers:Use (f(x+h) - f(x))/h so... (9 (x + h) + 8 - (9x + 8)) / h = (9x + 9h + 8 - 9x - 8) / h = 9h / h = 9

From Youtube

The Difference Quotient and Extrema Part 1 :I show you how the difference quotient was derived and also begin to explain the concept of extrema. Check out PatrickJMT and MathMikie.

Product and Quotient Laws of Logarithms Part1 :This lesson shows how to use the Product and Quotient Laws of Logarithms to simplify (and also how to) expand logarithmic expressions. This is the first part of a two part lesson. This lesson was created for the MHF4U Advanced Functions course in the province of Ontario, Canada.