[tex]\frac{dy}{dx} = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
[tex] = \lim_{h \to 0} \frac{(x + h)^{2} - 33(x + h) - 55 - x^{2} + 33x + 55}{h}[/tex]
[tex] = \lim_{h \to 0} \frac{x^{2} + 2xh + h^{2} - 33x - 33h - 55 - x^{2} + 33x + 55}{h}[/tex]
[tex] = \lim_{h \to 0} \frac{2xh + h^{2} - 33h}{h}[/tex]
[tex] = \lim_{h \to 0} 2x + h - 33[/tex]
[tex] = 2x - 33[/tex]
[tex]\text{At x = 22, } \frac{dy}{dx} = 2(22) - 33 = 44 - 33 = 11[/tex]
Thus, the slope at P is 11.
