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: $f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h} =$

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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 $3 - 2 x$ .

Steps

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 $- (x + h)^{2} + 3 (x + h) - (- x^{2} + 3 x)$ .

Step 3 ：Step 3: Divide the difference by $h$ to get the difference quotient, which is $\frac{- (x + h)^{2} + 3 (x + h) - (- x^{2} + 3 x)}{h}$ .

Step 4 ：Step 4: Take the limit as $h$ approaches 0 of the difference quotient to find the derivative, which is $3 - 2 x$ .

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 $3 - 2 x$ .

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)=−x2+3xStep 1:f(x+h)=Step 2:f(x+h)−f(x)=Step 3:f(x+h)−f(x)h=Step 4: f′(x)=limh→0f(x+h)−f(x)h=

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