SOLUTION: I need to find f(a), f(a+h), and the difference quotient f(a+h)- f(a)/h where h does not equal 0. my problem is f(x)=X^3

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Question 922835: I need to find f(a), f(a+h), and the difference quotient f(a+h)- f(a)/h where h does not equal 0.
my problem is f(x)=X^3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!




if f%28x%29=x%5E3 then
1. replace x with a
f%28a%29=a%5E3

2. replace x with a%2Bh
f%28a%2Bh%29=%28a%2Bh%29%5E3
f%28a%2Bh%29=%28a%2Bh%29%28a%2Bh%29%28a%2Bh%29 ...multiply all
f%28a%2Bh%29=a%5E3%2B3a%5E2%2Ah%2B3ah%5E2%2Bh%5E3


3. replace x with x%2Bh
f%28x%2Bh%29-f%28x%29%2Fh, h does not equal 0
f%28x%2Bh%29-f%28x%29%2Fh=%28%28x%2Bh%29%5E3-x%5E3%29%2Fh

f%28x%2Bh%29-f%28x%29%2Fh=%28h%5E3%2B3xh%5E2%2B3hx%5E2%29%2Fh
f%28x%2Bh%29-f%28x%29%2Fh=h%28h%5E2%2B3xh%2B3x%5E2%29%2Fh
f%28x%2Bh%29-f%28x%29%2Fh=cross%28h%29%28h%5E2%2B3xh%2B3x%5E2%29%2Fcross%28h%29
f%28x%2Bh%29-f%28x%29%2Fh=h%5E2%2B3xh%2B3x%5E2