Misread the question, doing qn 7 now.
To find the maximum and minimum value of a function, we need to take the first derivative of the function. This is also known as the slope or gradient of the function at a particular point of interest.
[tex]\frac{d}{dx}(e^{x}) = e^{x}[/tex]
To find the local maxima or minima, we need to set the first derivative to 0, because this will be a turning point in the graph.
[tex]e^{x} = 0[/tex], and since x doesn't have any value that equals 0, then we know there are no turning points in the graph.
Now, let's explore the endpoints, because those end points will be the maximum and minimum values.
At x = 4, [tex]y = e^{4}[/tex]
At x = -3, [tex]y = \frac{1}{e^{3}}[/tex]
So, our maximum point is at: [tex](4, e^{4})[/tex] and our minimum point is at: [tex](-3, \frac{1}{e^{3}})[/tex]
