SOLUTION: Find and simplify the difference quotient for the given function. f(x) = 6x2

Question 1176449: Find and simplify the difference quotient for the given function.
f(x) = 6x2

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

6x^2 is the same as writing

We replace every x with x+h

FOIL

Subtract f(x+h) and f(x). This is the "difference" portion of "difference quotient".

Distribute

The 6x^2 terms subtract and cancel.

Divide both sides by 'h'. This is where the "quotient" part comes in of "difference quotient".

Factor out h from the numerator

Cancel the pair of 'h' terms from the numerator and denominator

Answer:

Side note: Later in calculus you'll learn that as h approaches 0, the expression 12x+6h will approach 12x. This is the derivative of f(x) = 6x^2. Keep in mind that h = 0 is not allowed, since division by zero is not allowed, but we can get closer and closer to it.

RELATED QUESTIONS
Find and simplify the difference quotient for the given function. f(x) = x2 + 9x - 2 (answered by ewatrrr)

Please help me answer this question: Find and simplify the difference quotient... (answered by jim_thompson5910)

Find and simplify the difference quotient f(x+h)-f(x)/h, h#o for the given function... (answered by stanbon)

Find and simplify the difference quotient f(x+h)-f(x)/h for the function f(x) = x^2 + (answered by math_helper)

Find and simplify the difference quotient f(x+h)-f(h)/h ,h#0 for the given function.... (answered by josgarithmetic,ikleyn)

For the function f(x) = x2 + 5x - 5, find and simplify the difference quotient... (answered by Fombitz)

Find and simplify the difference quotient of f, f(x+h)-f(x)/h, h not= 0, for the... (answered by lynnlo)

Evaluate the difference quotient for the given function. Simplify your answer. f(x)=-x^3, (answered by Fombitz)

Find the difference quotient and simplify for the following function: f(x)=-10x^2 + 10x... (answered by josgarithmetic)