BC Calculus 402 MrG f'(x) and f"(x) Tests!

2959 days ago by MATH5H2013

#1)f(x)==(x-1)*(x-2)*(x-3)*(x-4)*(x-5), g(x)==f'(x), h(x)==f"(x) f(x)=(x-1)*(x-2)*(x-3)*(x-4)*(x-5) g(x)=diff(f(x),x) h(x)=diff(g(x),x) show(f(x)) show(g(x)) show(h(x)) show(expand(f(x))) show(expand(g(x))) show(expand(h(x))) 

#2) solve for x: f(x)==0 r1=solve(f(x)==0,x) show(r1) 
#2) solve for x: g(x)==0 r2=solve(g(x)==0,x) show(r2) show(r2[0]) show(r2[0].rhs()) show(r2[0].rhs().n()) show(r2[1].rhs().n()) show(r2[2].rhs().n()) show(r2[3].rhs().n()) 

#2) solve for x: h(x)==0 r3=solve(h(x)==0,x) show(r3) show(r3[0].rhs().n()) show(r3[1].rhs().n()) show(r3[2].rhs().n()) 

#3) graph f(x), g(x)=f'(x) and h(x)=f"(x) #3) f'(x) Test: You may have an extremum when f'(x) changes sign #3) f"(x) Test: If f'(a)=0 and f"(a)>0 Then f(a) is a Relative Minimum #3) f"(x) Test: If f'(a)=0 and f"(a)<0 Then f(a) is a Relative Maximum a=plot([f(x)],.99,5.01,color='red') b=plot([g(x)],.99,5.01,color='green') c=plot([h(x)],.99,5.01,color='orange') a+b+c