How do you find the max or minimum of #f(x)=-6x^2+9x#?

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Answer 1 · 2017-02-27T21:34:31

Maximum #->(x,y)=(3/4,27/8)#

The coefficient of #x^2# is negative so the graph is of form #nn# thus the vertex is a maximum.

The maximum is ta the vertex.

Write as: #y=-6(x^2-9/6x)#

#x_("vertex")=(-1/2)xx(-9/6) = + 9/12= 3/4#

By substitution we have:

#y_("vertex")=-6(3/4)^2+9(3/4)#

#y_("vertex")=+27/8#

Thus the maximum #->(x,y)=(3/4,27/8)#

Tony B