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How do you find the minimum and maximum value of #y=-(x-1)(x+4)#?

Answer 1

Isaiah Anthony

#y=-(x-1)(x+4) = -(x^2 + 3x - 4)#

Completing the square:

# = -((x + 3/2)^2 - 9 /4- 4)#

# = -((x + 3/2)^2 - 25 /4 )#

#implies y = -(x + 3/2)^2 + 25 /4 #

Now:

#(x + 3/2)^2 ge 0 qquad forall x#

#:. - (x + 3/2)^2 le 0 qquad forall x#

#:. y le 25/4 qquad forall x#

#implies {(y_("max") = 25/4),(y_("max") = - oo):}#

graph{-(x-1)(x+4) [-5, 5, -9.01, 9.01]}

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Answer 2

Avery Alexander

To find the minimum and maximum values of ( y = -(x - 1)(x + 4) ), you first need to determine the critical points by finding where the derivative is equal to zero. Then, you can use the second derivative test or examine the behavior of the function around those critical points to determine whether they correspond to minimum or maximum values.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.