Question

4x – 2y = cosy Find the derivative and clearly prove that y' is positive. What can you conclude about the graph of the given function?

Answer 1

- sides, we get - 4* = 2y + Cosy Apply derivative worto a on both ne 42 = die (2y +cosy) Using all at = at ln(a) Osina where é is a constant

and a la cosy = a sing du we get * 4* dn 4 = 2 dy - sing duy on ca

→ 4* ln (4) = (2-siny) aleye s olo = 4* e^(4) = (-3863)42 2-sing g-sinly) As sinly) range is [-1, 1], (2-sing) range Es [1,3] so denominator is always positive

z-sing and 4x is always positive for any value of a ,so (4) is always positive because both Numerator & denominator are always positive. ~ dy xo # (8,4) i.e. Es always positive implies y = f(x) increases monotonically ily increases continuously for increase in a.