f(x)=yf(x)=y
y=7x^4-6x^2+1y=7x4−6x2+1
dy/dx=28x^3-12xdydx=28x3−12x
dy/dx=0dydx=0
28x^3-12x=028x3−12x=0
7x^3-3x=07x3−3x=0
x(7x^2-3)=0x(7x2−3)=0
7x^2-3=07x2−3=0
7x^2=37x2=3
x^2=3/7x2=37
x=+-sqrt(3/7)x=±√37
x=0.655x=0.655 and x=-0.655x=−0.655 and x=0x=0
So the critical points of this equation is:
y=7(0.655)^4-6(0.655)^2+1=-0.286y=7(0.655)4−6(0.655)2+1=−0.286
y=7(-0.655)^4-6(-0.655)^2+1=4.863y=7(−0.655)4−6(−0.655)2+1=4.863
y=7(0)^4-6(0)^2+1=1y=7(0)4−6(0)2+1=1
Critical points:
(0.655, -0.286)(0.655,−0.286)
(-0.655, 4.863)(−0.655,4.863)
(0, 1)(0,1)
