Exponential Functions and Their Derivatives

Start by pressing RESET and then check the box for f(x) to see its graph in blue. Examine the graph of this function. Experiment with different values of the constant base b. Check on Tangent Line to see the graph of the tangent line at (a, f(a)), where a is controlled by the slider or input box. Check on Graph Shape? and answer the questions there about the shape of the graph and the shape of its derivative graph. Again, experiment with different values of b. Uncheck Graph Shape? and check f '(x) and Graph Conclusions. Uncheck Graph Conclusions and check Ratio. Uncheck Ratio and check Derivative Formula. Check Proof to see the proof.