1. The problem is to find the derivative of the function $f(x) = a \cdot x^2 + b \cdot x + c$ and then evaluate it at $x = 22$. 2. The formula for the derivative of a polynomial function $f(x) = a x^2 + b x + c$ is: $$f'(x) = 2 a x + b$$ This comes from the power rule: the derivative of $x^n$ is $n x^{n-1}$. 3. Applying the derivative formula to $f(x)$: $$f'(x) = 2 a x + b$$ 4. Now, evaluate the derivative at $x = 22$: $$f'(22) = 2 a \cdot 22 + b = 44 a + b$$ 5. So, the derivative of the function at $x=22$ is $44 a + b$. This means the slope of the tangent line to the curve at $x=22$ depends on the constants $a$ and $b$.