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−sin(x) e sin(x) + cos(x) 2 e sin(x)6.1 Introductory Calculus • 209Define 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, you can seethat f is increasing whenever f1 is positive, and that f is concave downwhenever 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 ) };⎛{1 √⎞ ⎛11 √⎞15 − 5 −⎜sol := arctan ⎝2 √ 2 2 ⎟ ⎜√ ⎠ , −arctan ⎝2 2 2 ⎟√ √ ⎠ + π,−2 + 2 5 −2 + 2 5arctan(− 1 2 − 1 √ 1 √ √5, − −2 − 2 5),2 2}arctan(− 1 2 − 1 √ 1 √ √5, −2 − 2 5)2 2Two of these solutions are complex.