(1 pt) Let Find all critical points and classify them as local maxima, local min

Question

(1 pt) Let Find all critical points and classify them as local maxima, local minima, saddle points, or none of these itical points andclassify them aslocalmaimacos(Sy) critical points: (0,0) give your points as a comma separated list of (x,y) coordinates. if your answer includes points that occur at a sequence of values, e.g., at every odd integer, or at any constant multiple of another value, use m for any non-zero even integer, n for any non-zero odd integer, and/or k for other arbitrary constants.) classifications: saddle point (give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)

Explanation / Answer

f(x,y) =1+3x²-cos(3y)

find partial derivative as

fx= 6x

fy= 3sin(3y)

Critical point is when fx =0 and fy=0

x= 0

and

sin(3y) =0

3y=kpi

y=(k*pi/3)

hence

Critical points :

(0, 2kpi/3) and (0, (2kpi+pi)/3)

Classifiacations :

Minimum, Saddle

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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