Answer:
[tex]x=-\frac{7}{2}[/tex] Extrema point.
The function does not have inflection points.
Step-by-step explanation:
To find the extrema points we have:
[tex]f'(x)=0[/tex]
Then:
[tex]f(x)=(2x+7)^4[/tex]
[tex]f'(x)=4(2x+7)^3(2)[/tex]
[tex]f'(x)=8(2x+7)^3[/tex]
Now:
[tex]f'(x)=8(2x+7)^3=0[/tex]
[tex]8(2x+7)^3=0[/tex]
[tex](2x+7)^3=0[/tex]
[tex]2x+7=0[/tex]
[tex]2x=-7[/tex]
[tex]x=-\frac{7}{2}[/tex]
To find the inflection points we need to calculate [tex]f''(x)=0[/tex] but due to that que have just one extrema point, the function does not have inflection points.
