Find the x-values of all points where the function has any relative extrema. Fin

Question

Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) =x^4 - 98x^2 + 2401 Select the correct choice below and if necessary fill in any answer boxes within your choice. The function has a relative maximum of at x = and a relative minimum of at x = (Use a comma to separate answers as needed) There are no relative minima. The function has a relative maximum of at x = (Use a comma to separate answers as needed) There are no relative maxima. The function has a relative minimum of at x= (Use a comma to separate answers as needed) There are no relative extrema.

Explanation / Answer

given f(x)=x4-98x2+2401

f '(x)=4x3-196x

for critical points, f '(x) =0

4x3-196x=0

4x(x2-49)=0

=>x=0, x=-7, x=7

f ''(x)=12x2-196

f ''(0)=12*02-196=-196<0

f(0)=2401

relative maximum of 2401 at x =0

f ''(-7)=12(-7)2-196 =392 >0

f(-7)=(-7)4-98(-7)2+2401 =0

relative minimum of 0 at x =-7

f ''(7)=12(7)2-196 =392 >0

f(7)=(7)4-98(7)2+2401 =0

relative minimum of 0 at x =7

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.