MAT 1300 Lecture Notes - Lecture 3: Asymptote

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Ex: find and classify all the relative extrema of f (x) = 3x4 + 16x3 30x2 9. Ex: use the second derivative test to nd and classify the critical points for f (x) = (x2 8x + 16)ex. Note that just because f(cid:48)(cid:48)(c) = 0 does not mean c is an in ection point. Ex: show that f (x) = x4 has a point c where the second derivative is zero but x = c is not an in ection point. One of the most applications of calculus is the determination of optimum ( min or max) value. Ex: we wish to enclose with a fence a rectangular region of 12,250 square feet next to a wall. The fencing for one side perpendicular to the wall costs $ 30/ft. Ex: a manufacturer wants to design an open box with a square base and a surface area of 108 in2. What is the maximum volume? h x x.

Related Questions

A. Find the critical points.

B. Use the second derivative test to

classify each critical point.

f (x, y) = âx^3 + 9xy â y^3

A. (1,1)and(0,0)

B. (3,3)and(0,0)

C. (1, 1) only
D. (-3, -3) and (0, 0)

E. (-3, -3) only

F. not listed

B. Which are true?

A. The critical points generate one relative maximum and one relative minimum. B. The critical points generate one relative maximum and one saddle point.

C. The critical points generate one relative minimum.
D. The critical points generate one relative minimum and one saddle point.

E. The second derivative test was inconclusive about all critical points.
F. None of the statements is true.

A. Find the critical points.

B. Use the second derivative test to

classify each critical point.

C. Find the relative extrema of the

function.

f(x,y)=2x^2âxy+y^2â3xây+3

A. (1, -2)
B. (2, -1)
C. (1, -1)
D. (1, 1)
E. Not listed

A. relative minimum at the critical point

B. relative maximum at the critical point

C. saddle point at the critical point
D. no result at the critical point

E. not listed

A. relative minimum value is 0
B. relative maximum value is 0
C. relative minimum value is 1
D. relative maximum value is 1
E. there are no relative extrema or the test failed at the critical point F. not listed.

MAT 1300 Lecture Notes - Lecture 3: Asymptote

MAT 1300 Full Course Notes

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