Question

Find all relative extrema and inflection points for fx)=(2x+7)^4

Answer 1

`x=-(7)/(2)` Extrema point.

The function does not have inflection points.

Explanation:

To find the extrema points we have:

`f'(x)=0`

Then:

`f(x)=(2x+7)^4`

`f'(x)=4(2x+7)^3(2)`

`f'(x)=8(2x+7)^3`

Now:

`f'(x)=8(2x+7)^3=0`

`8(2x+7)^3=0`

`(2x+7)^3=0`

`2x+7=0`

`2x=-7`

`x=-(7)/(2)`

To find the inflection points we need to calculate
`f''(x)=0` but due to that que have just one extrema point, the function does not have inflection points.