Calculus Examples

$y = e^{x}$

Step 1

Write $y = e^{x}$ as a function.

$f (x) = e^{x}$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$e^{x}$

Step 3

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$f'' (x) = e^{x}$

Step 4

To find the local maximum and minimum values of the function, set the derivative equal to $0$ and solve.

$e^{x} = 0$

Step 5

Since there is no value of $x$ that makes the first derivative equal to $0$ , there are no local extrema.

No Local Extrema

Step 6

No Local Extrema

Step 7