Question
find the difference quotient for f(x)=√x+2
Answers
GPT 3.5
To find the difference quotient for f(x) = √x + 2, we need to evaluate the expression [f(x+h) - f(x)] / h.
Step 1: Find f(x+h)
f(x+h) = √(x+h) + 2
Step 2: Compute f(x)
f(x) = √x + 2
Step 3: Subtract f(x) from f(x+h)
[f(x+h) - f(x)] = (√(x+h) + 2) - (√x + 2)
= √(x+h) - √x
Step 4: Divide by h
[f(x+h) - f(x)] / h = (√(x+h) - √x) / h
Therefore, the difference quotient for f(x) = √x + 2 is (√(x+h) - √x) / h.
Step 1: Find f(x+h)
f(x+h) = √(x+h) + 2
Step 2: Compute f(x)
f(x) = √x + 2
Step 3: Subtract f(x) from f(x+h)
[f(x+h) - f(x)] = (√(x+h) + 2) - (√x + 2)
= √(x+h) - √x
Step 4: Divide by h
[f(x+h) - f(x)] / h = (√(x+h) - √x) / h
Therefore, the difference quotient for f(x) = √x + 2 is (√(x+h) - √x) / h.