CPM Homework Help : PC Problem 11-58

Use the limit definition of the derivative to find the general slope function for $f\left(x\right) = x^{2} + 3x$ .

Hint:

$f'(x)=\lim\limits_{ h \to 0 }\frac{f(x+h)-f(x)}{h}$

Step 1:

$f'(x)=\lim\limits_{ h \to 0 }\frac{((x+h)^2+3(x+h))-(x^2+3x)}{h}$

Now simplify and to find the limit.