SOLUTION: For the function f(x,y)=x^2+2y^2, find f(x+h,y)- f(x,y)/ (h) The answer is 2x+h, how do I get this. Thank You

Question 585258: For the function f(x,y)=x^2+2y^2, find
f(x+h,y)- f(x,y)/ (h)
The answer is 2x+h, how do I get this.
Thank You
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
f(x,y)=x^2+2y^2

f(x+h,y)=(x+h)^2+2y^2

f(x+h,y)=x^2+2xh+h^2+2y^2

-------------------------------------------------------

( f(x+h,y)- f(x,y) )/h

( (x^2+2xh+h^2+2y^2)- (x^2+2y^2) )/h

( x^2+2xh+h^2+2y^2 - x^2-2y^2 )/h

( 2xh + h^2 )/h

( h(2x+h) )/h

2x+h

So ( f(x+h,y)- f(x,y) )/h = 2x+h where f(x,y)=x^2+2y^2
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