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

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Answer 1 · 2018-07-28T23:20:58

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

# = -((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]}