Gradient of a tangent from first principles
Use the displayed polynomial rule
\[q(x)=x^2 + x + 3\]
The target value is shown below. Use the limit definition of the derivative
\[x=-2\]
The difference quotient is
\[\frac{q(x+h)-q(x)}{h}\]
Use the displayed polynomial rule
The target value is shown below. Use the limit definition of the derivative
The difference quotient is