Calculus UNIT206 HWK p114

2815 days ago by MATH4R2013

#15) p114 is f(x)=3*x-2*abs(x)-1 differentiable everywhere? If not, state why not. f(x)=3*x-2*abs(x)-1 plot(f(x),-5,5) 
       
#20) p114 estimate f'(0) using h=.001 f(x)=x^3-4*x g(x)=(f(x+.001)-f(x))/.001 show(g(0)) 
       
#25) p114 estimate f'(0) using h=.001 f(x)=x^(2/5) g(x)=(f(x+.001)-f(x))/.001 show(g(0)) 
       
#30) p114 do you recognize f'(x) when f(x)=-ln(cos(x))? f(x)=-log(cos(x)) g(x)=diff(f(x),x) show(g(x)) 
       
#35) p114 f(x) f1(x)=(x+1)^2 f2(x)=2*x+1 f3(x)=(4-x)^2 f=piecewise([[(-2,0),f1],[(0,3),f2],[(3,6),f3]]) p1=plot(f,color='red') #35 p114 f'(x) f1(x)=2*x+2 f2(x)=2 f3(x)=2*x-8 f=piecewise([[(-2,0),f1],[(0,3),f2],[(3,6),f3]]) p2=plot(f,color='green') p1+p2 
       
#45) p114 f(x) f1(x)=2*x+1 f2(x)=x^2+1 f=piecewise([[(-3,0),f1],[(0,3),f2]]) p1=plot(f,color='red') #45 p114 f'(x) f1(x)=2 f2(x)=2*x f=piecewise([[(-3,0),f1],[(0,3),f2]]) p2=plot(f,color='green') p1+p2