kirstenrewis
kirstenrewis kirstenrewis
  • 12-01-2017
  • Advanced Placement (AP)
contestada

I reallllllyyy need help, it's literally my last question and Im stuck on it.
f(0)=3
f'(0)=5
f"(0)=7
h(x)=cos(kx)[f(x)]+sinx
Find h'(x) at x=0.

Respuesta :

bartdrinksmalk
bartdrinksmalk bartdrinksmalk
  • 12-01-2017
We have
[tex]h(x)=\cos (kx)*f(x)+\sin x[/tex]

We take the derivative of [tex]h(x)[/tex]:
[tex]h'(x)=\cos (kx)*f'(x)+k(-\sin (kx))*f(x)+\cos x[/tex]

Now we simply plug in 0:
[tex]h'(0)=\cos (k*0)*f'(0)-k\sin (k*0)*f(0)+\cos 0[/tex]
[tex]=\cos 0 *5-k\sin 0 *3+\cos 0[/tex]
[tex]=5*1-3k*0+1[/tex]
[tex]=5+1[/tex]
[tex]=6[/tex]
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