Let f(x)=x^2+2x-7. find the difference quotient for this function.
Please help me understand step by step
Please help me understand step by step
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you want [ f(x+h) – f(x) ] / h, so
[ (x+h)² + 2(x+h) – 7 – (x² + x – 7) ] / h =
[ x² + 2hx + h² + 2x + 2h – 7 – x² – x + 7 ] / h =
[ 2hx + 2h + h² ] / h =
...{notice all the non-h terms canceled out }
2x + 2 + h
[ (x+h)² + 2(x+h) – 7 – (x² + x – 7) ] / h =
[ x² + 2hx + h² + 2x + 2h – 7 – x² – x + 7 ] / h =
[ 2hx + 2h + h² ] / h =
...{notice all the non-h terms canceled out }
2x + 2 + h