let's use this x right over here and notice we don't even have to figure out what the axis 'cause we know but if it ended overhears four-fifths the speed of both the sba science going to be the size of the three fifths of the course i was going to be forecast or which will give some actual point or the tenant could be for three-fourths and then the side will be negative benefits and of course i will be negative forfeit so let's use these overuse of the middle of is going to be equal to three plus went two times coastline of x_ were using this one over here so to transpose side of exco sign of experience negative four fists negative for fests and then plus three halves plus three has times in the sign of x sinai lectures negative three fifths negative three fits and what is this going to be equal to this is going to be equal to three plus this is negative eight fifths dreamweaver should write three minus eight fifth three minus the this minus nine tenths minus nine tenths and so this is going to be equal to we could put everything over ten thirty over ten minus sixteen over ten right that's eight fists minus nine or ten and this gives us what this gives us five or ten five over ten or or one-half so the minimum value the minimum value for denominator everything we've been dealing with so far has been our denominator the middle of the idea of all of this business over here the minimum value is one-half so the maximum value that this whole expression takes is when the minimum values one out so we get one over one-half equal to to we're done