Calculus, 2ADV C3 2020 HSC 10 MC The graph shows two functions `y = f(x)` and `y = g(x)`. Define `h(x) = f(g(x))`. How many stationary points does `y = h(x)` have for `1 <= x <= 5`? 0 1 2 3 Show Answers Only `D` Show Worked Solution `h(x) = f(g(x))`♦♦♦ Mean mark 11%. `h′(x) = g′(x) xx f′(g(x))` `text(S.P.’s occur when)\ \ g′(x) = 0\ \ text(or)\ \ f′(g(x)) = 0` `g′(x) = 0\ \ text(when)\ \ x =3\ (text(from graph))` `f′(x) = 0\ \ text(when)\ \ x ~~ 1 \ \ text{(i.e.}\ xtext{-value is just under 1)}` `text(Find values of)\ x\ text(when)\ g(x) ~~ 1:` `text(By inspection, there are 2 values where)` `g(x) ~~ 1, \ x ∈ [1, 5]` `:.\ text(There are 3 S.P.’s for)\ y = h(x), \ x ∈ [1, 5]` `=> D`