Nilai maksimum dari f(x) = 17 sin x + 144 cos x adalah

<p>nilai maksimum diperoleh saat f'(x) = 0</p><p>&nbsp;</p><p>f(x) = u + v &nbsp; &nbsp; &nbsp;------&gt; &nbsp;f'(x) = u'.v + v'.u</p><p>u = 17 sin x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;u' = 17 cos x</p><p>v = 144 cos x &nbsp; &nbsp; &nbsp; &nbsp;v' = -144 sinx</p><p>u'.v = 17 .cos x. 144 cos x = 17 . 144 . cos²x</p><p>v'.u = -144. sin x. 17 . sin x = -17. 144. sin²x</p><p>f'(x) = u'.v + v'.u</p><p>&nbsp; &nbsp; 0 &nbsp; = 17 . 144 . cos²x - 17 . 144. sin²x</p><p>------------------------------------------------ : 17 .144</p><p>&nbsp; &nbsp; 0 &nbsp; = &nbsp;cos²x &nbsp;- sin²x</p><p>ubah cos²x &nbsp;- sin²x ke bentuk 1-2 sin²x atau 2 cos²x - 1</p><p>&nbsp; &nbsp; 0 &nbsp; = 2 cos²x - 1</p><p>&nbsp; &nbsp; 1 &nbsp; = 2 cos²x</p><p>&nbsp; 1/2 = cos²x</p><p>&nbsp;(√2)/2 = cos x</p><p>&nbsp;45 = x</p><p>masukan nilai x = 45 ke persamaan awal</p><p>f(x) = 17 sin 45 + 144 cos 45</p><p>&nbsp; &nbsp; &nbsp; &nbsp; = 17 . (√2)/2 &nbsp;+ 144 . (√2)/2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; = (161√2)/2</p><p>jadi nilai maksimum dari persamaan tadi adalah (161√2)/2</p>