Find and simplify the difference quotient $\frac{f (x + h) - f (x)}{h}, h \neq 0$ for the given function
$f (x) = 5 x^{2}$
$\frac{f (x + h) - f (x)}{h} = ◻ (Simplify your answer.)$

Answer

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Answer

The simplified difference quotient is $5 h + 10 x$ .

Steps

Step 1 ：Substitute $x + h$ into the function to get $f (x + h) = 5 (x + h)^{2}$ .

Step 2 ：Subtract $f (x)$ from this to get $f (x + h) - f (x) = 5 (x + h)^{2} - 5 x^{2}$ .

Step 3 ：Divide this by $h$ to get the difference quotient.

Step 4 ：Simplify the difference quotient to get $5 h + 10 x$ .

Step 5 ：The simplified difference quotient is $5 h + 10 x$ .