Question

The function f(x) = 9x + 2x ^ - 1 * as one local minimum and one local maximum This function has a local maximum at x =

Answer 1

Step-by-step explanation

To solve the question, we will make use of the graph of the function

`f(x)=9x+2x^(-1)`

The graph of the function is shown below

From the graph

Looking at a graph, the local maxima and minima are the points where the graph flattens out and changes from increasing to decreasing or vice versa. When the graph is flat, that means the slope is zero.

`\mathrm{Extreme\:Points\:of}\:9x+2\cdot (1)/(x):\quad \mathrm{Maximum}\left(-(√(2))/(3),\:-6√(2)\right),\:\mathrm{Minimum}\left((√(2))/(3),\:6√(2)\right)`

Therefore, the function has a local maximum at

`x=(-√(2))/(3)`

with a value of

`-6√(2)`

For the local minimum

The function has a local minimum at

`x=(√(2))/(3)`

with a value of

`6√(2)`