Edexcel A Level - Exponential & Log Basics

Exponential Functions, Logs & Log Laws

Exponential Graphs: ${a^x}$
The graph of $\color{blue}{ f(x) = {a^x} }$ is shown in blue, together with its tangent and gradient at a sample point in red.

By considering the gradient at x = 0, 1, 2, 3, can you predict what the gradient function of $\color{blue}{ f(x) = {a^x} }$ is?
Gradients of ${a^x}$ and ${e^x}$
Compare the graph of $$\color{blue}{ f(x) = {a^x} }$$ with the graph of its gradient function, $$\color{green}{ f'(x) }$$.
Adjust the value of a till the the two curves coincide.