What is the gradient of the chord \(AB\)?
\[\begin{align*}
\text{gradient of } AB &= \dfrac{f(x+h) - f(x)}{x+h - x} \\
&=\dfrac{a^{x+h} - a^x}{h}
\end{align*}\]
This expression gives us the gradient of \(AB.\) If \(h\) is small enough, then this also gives us an estimation of the gradient of \(f(x)\) at \(A.\)
How could we find the exact gradient at \(A\)? See the gradient of \(a^x\) to find out.
