The function is f (x) =3sinx+cos2x f'(x)=3cosx-2sin2x f"(x)=-3sinx-4cos2x Is this right?
F fgmango New member Joined Oct 13, 2005 Messages 11 Nov 14, 2005 #1 The function is f (x) =3sinx+cos2x f'(x)=3cosx-2sin2x f"(x)=-3sinx-4cos2x Is this right?
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Nov 14, 2005 #2 Looks good to me. Eliz.
F fgmango New member Joined Oct 13, 2005 Messages 11 Nov 14, 2005 #3 I'm having trouble finding the x-int f"(x)=-3sinx-fcos2x = -sinx(3+4sinx) -sinx=0 3+4sinx=o sinx=0 4sinx=-3 sinx=-3/4 Is this right?
I'm having trouble finding the x-int f"(x)=-3sinx-fcos2x = -sinx(3+4sinx) -sinx=0 3+4sinx=o sinx=0 4sinx=-3 sinx=-3/4 Is this right?
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Nov 14, 2005 #4 What is the "f" in "-3sin(x) - fcos(2x)"? How are you getting that 4cos(2x) equals 4sin<sup>2</sup>(x)? Eliz.
What is the "f" in "-3sin(x) - fcos(2x)"? How are you getting that 4cos(2x) equals 4sin<sup>2</sup>(x)? Eliz.
F fgmango New member Joined Oct 13, 2005 Messages 11 Nov 14, 2005 #5 That f is suppose to be a 4. I was trying to substite in cos2x=1+sinx
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Nov 14, 2005 #6 You might want to check your identities: cos(2x) = 1 + sin<sup>2</sup>(x). Eliz.
F fgmango New member Joined Oct 13, 2005 Messages 11 Nov 14, 2005 #7 Right my mistake. Thats how I was trying to factor out -sinx.
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Nov 14, 2005 #8 Hello, fgmango! I'm having trouble finding the x-int Click to expand... No wonder! . . . You're solving: f′′(x) = 0\displaystyle f''(x)\,=\,0f′′(x)=0 . . You're looking for inflection points! f′′(x) = −3⋅sin(x) − 4⋅cos(2x) = 0\displaystyle f''(x)\:=\:-3\cdot\sin(x)\,-\,4\cdot\cos(2x)\:=\:0f′′(x)=−3⋅sin(x)−4⋅cos(2x)=0 Then: .-3⋅sin(x) − 4[1 − 2⋅sin2(x)] = 0\displaystyle 3\cdot\sin(x)\,-\,4[1\,-\,2\cdot\sin^2(x)]\:=\:03⋅sin(x)−4[1−2⋅sin2(x)]=0 We have a quadratic: .8⋅sin2(x) − 3⋅sin(x) − 4 = 0\displaystyle 8\cdot\sin^2(x)\,-\,3\cdot\sin(x)\,-\,4\:=\:08⋅sin2(x)−3⋅sin(x)−4=0 . . with roots: .sin(x) = 3 ± 13716\displaystyle \sin(x)\:=\:\frac{3\,\pm\,\sqrt{137}}{16}sin(x)=163±137 Inflection points occur at: .x = arcsin(3 ± 13716)\displaystyle x\;=\;\arcsin\left(\frac{3\,\pm\,\sqrt{137}}{16}\right)x=arcsin(163±137) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ If you're really looking for x\displaystyle xx-intercepts, set f(x) = 0.\displaystyle f(x)\,=\,0.f(x)=0. We have: .3⋅sin(x) + cos(2x) = 0\displaystyle 3\cdot\sin(x)\,+\,\cos(2x)\:=\:03⋅sin(x)+cos(2x)=0 Then: .3⋅sin(x) + [1 − 2⋅sin2(x)] = 0\displaystyle 3\cdot\sin(x)\,+\,[1\,-\,2\cdot\sin^2(x)]\:=\:03⋅sin(x)+[1−2⋅sin2(x)]=0 We have a quadratic: .2⋅sin2(x) − 3⋅sin(x) − 1 = 0\displaystyle 2\cdot\sin^2(x)\,-\,3\cdot\sin(x)\,-\,1\:=\:02⋅sin2(x)−3⋅sin(x)−1=0 . . with roots: .sin(x) = 3 ± 174\displaystyle \sin(x)\;=\;\frac{3\,\pm\,\sqrt{17}}{4}sin(x)=43±17 x\displaystyle xx-intercepts occur at: .x = arcsin(3 ± 174)\displaystyle x\:=\:\arcsin\left(\frac{3\,\pm\,\sqrt{17}}{4}\right)x=arcsin(43±17) *
Hello, fgmango! I'm having trouble finding the x-int Click to expand... No wonder! . . . You're solving: f′′(x) = 0\displaystyle f''(x)\,=\,0f′′(x)=0 . . You're looking for inflection points! f′′(x) = −3⋅sin(x) − 4⋅cos(2x) = 0\displaystyle f''(x)\:=\:-3\cdot\sin(x)\,-\,4\cdot\cos(2x)\:=\:0f′′(x)=−3⋅sin(x)−4⋅cos(2x)=0 Then: .-3⋅sin(x) − 4[1 − 2⋅sin2(x)] = 0\displaystyle 3\cdot\sin(x)\,-\,4[1\,-\,2\cdot\sin^2(x)]\:=\:03⋅sin(x)−4[1−2⋅sin2(x)]=0 We have a quadratic: .8⋅sin2(x) − 3⋅sin(x) − 4 = 0\displaystyle 8\cdot\sin^2(x)\,-\,3\cdot\sin(x)\,-\,4\:=\:08⋅sin2(x)−3⋅sin(x)−4=0 . . with roots: .sin(x) = 3 ± 13716\displaystyle \sin(x)\:=\:\frac{3\,\pm\,\sqrt{137}}{16}sin(x)=163±137 Inflection points occur at: .x = arcsin(3 ± 13716)\displaystyle x\;=\;\arcsin\left(\frac{3\,\pm\,\sqrt{137}}{16}\right)x=arcsin(163±137) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ If you're really looking for x\displaystyle xx-intercepts, set f(x) = 0.\displaystyle f(x)\,=\,0.f(x)=0. We have: .3⋅sin(x) + cos(2x) = 0\displaystyle 3\cdot\sin(x)\,+\,\cos(2x)\:=\:03⋅sin(x)+cos(2x)=0 Then: .3⋅sin(x) + [1 − 2⋅sin2(x)] = 0\displaystyle 3\cdot\sin(x)\,+\,[1\,-\,2\cdot\sin^2(x)]\:=\:03⋅sin(x)+[1−2⋅sin2(x)]=0 We have a quadratic: .2⋅sin2(x) − 3⋅sin(x) − 1 = 0\displaystyle 2\cdot\sin^2(x)\,-\,3\cdot\sin(x)\,-\,1\:=\:02⋅sin2(x)−3⋅sin(x)−1=0 . . with roots: .sin(x) = 3 ± 174\displaystyle \sin(x)\;=\;\frac{3\,\pm\,\sqrt{17}}{4}sin(x)=43±17 x\displaystyle xx-intercepts occur at: .x = arcsin(3 ± 174)\displaystyle x\:=\:\arcsin\left(\frac{3\,\pm\,\sqrt{17}}{4}\right)x=arcsin(43±17) *