Find the difference quotient and simplify your answer. f(x)=2x^2+3x-1, (f(x+h)-f(x))/h h does not equal zero

magda8471

magda8471

Answered question

2022-08-05

Find the difference quotient and simplify your answer.
f ( x ) = 2 x 2 + 3 x 1 , f ( x + h ) f ( x ) h h does not equal zero

Answer & Explanation

optativaspv

optativaspv

Beginner2022-08-06Added 14 answers

F ( x + h ) = 2 ( x + h ) 2 + 3 ( x + h ) 1
to get that i just plugged x+h into where x was.
so: 2 ( x + h ) 2 + 3 ( x + h ) 1 ( 2 ( x ) 2 + 3 x 1 ) h
now factor everything: 2 ( x 2 + 2 x h + h 2 ) + 3 x + 3 h 1 ( 2 x 2 + 3 x 1 ) h
then: 2 x 2 + 3 x + 4 x h + 2 h 2 + 3 h 1 2 x 2 3 x + 1 h
now combine like terms and you are left with: 4 x h + 2 h 2 + 3 h h
factor out an h: h ( 2 h + 4 x + 3 ) h
cancel out the h's and you are left with 2h+4x+3
cortejosni

cortejosni

Beginner2022-08-07Added 5 answers

2 ( x + h ) 2 + 3 ( x + h ) 1 ( 2 x 2 + 3 x 1 ) h
You place (x + h) in all the x variables for the firstpart. After that it states that -f(x), so you state theoriginal function. All of this is divided by h.
After this you just solve.
2 ( x 2 + 2 h x + h 2 ) + 3 x + 3 h 1 2 x 2 3 x + 1 h
2 x 2 + 4 h x + 2 h 2 + 3 x + 3 h 1 2 x 2 3 x + 1 h
- cancel everything that cancles
4 x h + 2 h 2 + 3 h h
h ( 4 x + 2 h + 3 ) h
4x + 2h + 3 = answer

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