Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.)
\[
f(x)=-x^{2}+3 x
\]
Step 1:
\[
f(x+h)=
\]
Step 2:
\[
f(x+h)-f(x)=
\]
Step 3:
\[
\frac{f(x+h)-f(x)}{h}=
\]
Step 4: $\quad f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=$
Answer
Final Answer: The slope of the tangent line to the graph of the function at any point is given by the derivative of the function, which is \(\boxed{3 - 2x}\).
Step 1 ：Step 1: Calculate \(f(x+h)\), which is \(- (x+h)^{2} + 3(x+h)\).
Step 2 ：Step 2: Find the difference \(f(x+h) - f(x)\), which is \(- (x+h)^{2} + 3(x+h) - (-x^{2} + 3x)\).
Step 3 ：Step 3: Divide the difference by \(h\) to get the difference quotient, which is \(\frac{- (x+h)^{2} + 3(x+h) - (-x^{2} + 3x)}{h}\).
Step 4 ：Step 4: Take the limit as \(h\) approaches 0 of the difference quotient to find the derivative, which is \(3 - 2x\).
Step 5 ：Final Answer: The slope of the tangent line to the graph of the function at any point is given by the derivative of the function, which is \(\boxed{3 - 2x}\).
