### Calculus of Trigonometry & Logarithms

We have found that the gradient function of $a^x$ can be written as $f'(x) = a^x\times f'(0),$
i.e. the gradient function is the function itself multiplied by a constant, and this constant is the gradient of $a^x$ at $x = 0$. There will be a special case when $f'(0) = 1$ as then the gradient function of $a^x$ would be itself, $a^x$.
Before using the applet, look at the values given. Approximately what value do you think $a$ will take to give $f'(0) \approx 1?$
Use the slider to find the value of $a$ when $f'(0) \approx 1$.