Tentukan - Universityku

1.turunan pertama dan kedua
2.titik stasioner
3. nilai maksimum dan minimum dari;
f(x)=4cos (4x-pi/2)

Tentukan

Jawaban:

$f(x) = 4 cos(4x - frac{pi}{2} ) \ f'(x) = 4. - sin(4x - frac{pi}{2} ) \ = - 4 sin(4x - frac{pi}{2} ) \ f''(x) = 4. - 4 cos(4x - frac{pi}{2} ) \ = - 16 cos(4x - frac{pi}{2} )$

Titik stasioner, maka f'(x) = 0

$f'(x) = - 4 sin(4x - frac{pi}{2} ) \ 0 = - 4 sin(4x - frac{pi}{2} ) \ - - - - - - - - div - 4 \ 0 = sin(4x - frac{pi}{2} ) \ sin(0) = sin(4x - frac{pi}{2} ) \ 4x - frac{pi}{2} = 0° + kpi \ 4x = frac{pi}{2} + 0° + kpi \ 4x = frac{pi}{2} + kpi \ - - - - - - - div 4 \ x = frac{1}{8} pi + frac{1}{4} kpi$

maka nilai x yang memenuhi persamaan diatas sekaligus menjadi titik stasionernya

$x = frac{1}{8} pi.......(k = 0) \ x = frac{3}{8} pi.......(k = 1) \x = frac{5}{8} pi.......(k = 2) \ x = frac{7}{8} pi.......(k = 3) \ x = frac{9}{8} pi.......(k = 4) \ x = frac{11}{8} pi.......(k = 5) \ x = frac{13}{8} pi.......(k = 6) \ x = frac{15}{8} pi.......(k = 6)$