Maple 9 Learning Guide - Maplesoft

7.1 Introductory Calculus • 219In this case, the second derivative exists.> diff( f(x), x, x );−sin(x) e sin(x) + cos(x) 2 e sin(x)Define the function f2 to be the second derivative of f.> f2 := unapply( %, x );f2 := x → −sin(x) e sin(x) + cos(x) 2 e sin(x)When you plot f and its first and second derivatives, f is increasingwhenever f1 is positive, and f is concave down whenever f2 is negative.> plot( [f(x), f1(x), f2(x)], x=0..10 );210–12 4 6 8 10x–2The graph of f has an inflection point where the second derivativechanges sign, and the second derivative can change sign at the values ofx where f2(x) is zero.> sol := { solve( f2(x)=0, x ) };