#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)
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#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))
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#25) p114 estimate f'(0) using h=.001
f(x)=x^(2/5)
g(x)=(f(x+.001)-f(x))/.001
show(g(0))
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#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))
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#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
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#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
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