1.) Suppose that the function f has the following characteristics: then A. f has

Question

1.) Suppose that the function f has the following characteristics:

then

A. f has a local minimum at x = 1

B. f has a local maximum at x = 1

C. f has neither a local maximum or a local minimum at x = 1

D. there is not enough information to determine if x = 1 is a maximum or minimum

2.) Find the distance from the origin to the point on the line y = -2x + 3 that is closest to the origin. Round to two decimal places.

3.) Suppose you need to build a box with no top from a square sheet of metal by cutting squares of equal size out of each corner and folding up the flaps to form the four sides of the box. Find the maximum possible volume in cubic inches of such a box if the square sheet of metal is 100 inches on each side. Round to two decimal places.

Explanation / Answer

1)If there exists a positive number r such that for every x in (a - r, a] we have f'(x) ? 0, and for every x in [a, a + r) we have f'(x) ? 0, then f has a local maximum at a

hence option B is correct

2) distance is gievn by : 3/sqrt(1+2^2)

=3/sqrt(5

3) let the length of squares cut out be 'a'

then volume of box will be:V=(100-2a)a

to find maximum volume we differentiate above expression:

V'=100-4a

V'=0

=> a=25

Hence maximum volume is:25*(100-2*25)=50*25=1250

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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