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Chapter 12: Q 8. (page 916)

Find the range of the function fx,y=-8xx2+y2+1from Example 4 by finding the largest value, M, and smallest value, m, of c for which the equation-8xx2+y2+1=c

has a solution. (Hint: Find the two values for c such that the

level 鈥渃urves鈥� are a single point. Then show that the given

equation has a solution for every value of c between those two

values.)

Short Answer

Expert verified

Range is-4,4

Step by step solution

01

Step 1. Given information

Function isfx,y=-8xx2+y2+1

02

Step 2. Explanation

-8xx2+y2+1=ccx2+y2+1=-8xx2+8cx+y2+1=0x2+2路4c路x+4c2+y2+1-4c2=0x+4c2+y2+1-16c2=0

Here,

16c2-1>0c2<16c鈭�-4,4

So, range is -4,4.

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