SOLUTION: Where do I start? I am so lost... here is the problem... Given f(x)=6x^2 + 5x - 4 find [f(x+h)-f(x)] / h

Algebra ->  Rational-functions -> SOLUTION: Where do I start? I am so lost... here is the problem... Given f(x)=6x^2 + 5x - 4 find [f(x+h)-f(x)] / h       Log On


   

Question 15182: Where do I start? I am so lost... here is the problem...
Given f(x)=6x^2 + 5x - 4 find [f(x+h)-f(x)] / h
Answer by wgunther(43) About Me  (Show Source):
You can put this solution on YOUR website!
okay f%28x%29=6x%5E2+%2B+5x+-+4+
x is just the dependent variable. you can just as easily say
f%28a%29=6a%5E2+%2B+5a+-+4
or
f%282%29=6%282%29%5E2+%2B+5%282%29+-+4
That's just input. Now, the problem you are asking is VERY important for later mathematics, so spend some time trying to understand it for sure.
+%28f%28x%2Bh%29-f%28x%29%29+%2F+h
so
+%28%286%28x%2Bh%29%5E2+%2B+5%28x%2Bh%29+-+4%29-%286x%5E2+%2B+5x+-+4%29%29%2Fh+
+%28+6%28x%5E2+%2B+2xh+%2B+h%5E2%29+%2B+5x+%2B+5h+-+4+-+6x%5E2+-+5x+%2B+4%29%2Fh+
REMEBER TO DISTRIBUTE NEGATIVE IN SECOND TERM!
+%28+6x%5E2%2B12xh%2B6h%5E2+%2B+5x+%2B+5h+-+4+-+6x%5E2+-+5x+%2B+4%29%2Fh+
Combined any common terms (6x^2-6x^2=0, 5x-5x=0 -4+4=0)
+%28+12xh+%2B+6h%5E2+%2B+5h%29%2Fh+
Factor out and cancel out h
+%28+h%2812x+%2B+6h+%2B+5%29%29%2Fh+
++12x+%2B+6h+%2B+5+
Like I said, this is a very important thing for later mathematical concept. It's called the difference quotient.