Just some math problems

9514 1404 393

  (min, max) are exact or rounded to thousandths, so you can round as may be required

  5.  (10.607, 14.229)

  6.  (-1.586, -0.764)

  7.  (4, 5.211)

  8.  (-3.5, -2.342)

Step-by-step explanation:

Given:

  the attached function definitions and intervals

Find:

  the minimum and maximum on the given interval

Solution:

In a couple of cases, the coefficient of x is negative, indicating the basic square root function has been reflected over the y-axis. That will put the maximum at the left end of the interval, instead of the right end, where it would otherwise be.

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5. minimum: f(3.5) = 5√(3.5+1) +1 = 5√4.5 +1 = 10.607

  maximum: f(6) = 5√(6+1) +1 = 5√7 +1 = 14.229

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6. minimum = f(-2) = √(-(-2)) -3 = √2 -3 = -1.586

  maximum = f(-5) = √(-(-5)) -3 = √5 -3 = -0.764

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7. minimum = f(-6) = 2√(3 -(-6)) -2 = 2√9 -2 = 4

 maximum = f(-10) = 2√(3 -(-10)) -2 = 2√13 -2 = 5.211

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8. minimum = f(0) = (1/2)√(0 +1) -4 = -3.5

  maximum = f(10) = (1/2)√(10+1) -4 = (1/2)√11 -4 = -2.342

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