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

Answer

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Answer

The simplified difference quotient is $\boxed{5h + 10x}$.

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 $f(x+h) - f(x) = 5(x+h)^2 - 5x^2$.

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

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

Step 5 ：The simplified difference quotient is $\boxed{5h + 10x}$.