How do you find the point on the graph of #x^2−2x=15−y^4# has the largest y-coordinate?

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Answer 1 · 2015-02-25T15:22:46

Start by solving a simpler equation:
#x^2−2x = 15−f(x)#
which simplifies to
#f(x) = -x^2 + 2x + 15#

#f(x)# takes on a maximum value when
#f'(x) = 0#
that is when
#-2x + 2 = 0#
#rarr x = 1#

Note that if #f(x) = y^4#
a maximum value of #f(x)# implies a maximum value of #y^4# provided #f(x) >= 1#

Using #x=2# in the original equation gives
#y^4 = 16#
and therefore (since we are only interested in the largest value for #y#

#y = 2#