Question

state the maximum number of turns in the graph of functions
f(x)=x^4+2x^2+4??

Answer 1

\[f(x)=x^4+2x^2+4\]
\[f'(x)=4x^3+4x\]
\[f''(x)=12x^2+4\]
At S.P's (Stationary Points) f'(x)=0
\[4x^3+4x=0\]
\[x(x^2+1)=0\]
\[x=0\]
\[y=4\]
\[f''(x)=12(0)^2+4\]
\[=4\]
\[>0\]
Therefore minimum turning point at (0, 4)
Therefore there is only 1 turn in the function.