11.1    a) tangent line of x^2+2x at (2,8)
        b) tangent line of 1/3*x^3-5x at (3,-6)
        c) tangent line of 2+(x-1)^(1/3) at (1,2)
           limit (2+(x-1)^(1/3))' at x to 1+
           limit 2+(-1 + y)^(1/3)+1/(3 (-1 + y)^(2/3))(x-y) where y to 1+

11.2    a) solve (x^2-2x)'=2
           tangent line of x^2-2x at x=2
        b) solve (sqrt(2x-9))'=1
           tangent line of sqrt(2x-9) at x=5

11.3    tangent line of 2+1/x at (1,3)
        plot 4-x where x=-1..5

11.4    tangent line of sqrt(25-x^2) at (3,4)

11.5    a) monotonicity x^3-3x^2
        b) monotonicity 8x^2-x^4
        c) monotonicity x-sin(x)
        d) monotonicity x/ln(x)
        e) monotonicity x*e^(-x)

11.6    a) local extrema x^3-3x
        b) local extrema 6x^4-x^6
        c) local extrema 5x^6-6x^5
        d) local extrema x*ln(x)
        e) local extrema (x^2-1)^4
        f) local extrema x*(ln(x))^2
        g) local extrema x^2*e^(-x)
        h) local extrema x-arctan(x)

11.7    a) global extrema x^2-2x+3 where x=0..5
        b) global extrema x^3-3x+1 where x=-2..0
        c) global extrema 4x^6-24x^4 where x=-1..3
        d) global extrema x-ln(x) where x=1/e..e

11.8    maximum (9-2x)^2*x

11.9    cos(pi/2-arccos(0.6))
        extrema x/5+sqrt(x^2+1-1.6x)/4

11.10   a) Plot[Piecewise[{{1+x, 0<=x<2}, {3*(x-3)^2, 4>x>=2}, {5+1/(x-4.5), 4.5>x>=4}, {1+1/(5-x), 5>x>=4.5}, {1, 5.1>x=>5}}],{x,0,5.1}]
        b) Plot[Piecewise[{{1+1/(2-x), -2<=x<2}, {1, 2.1>x>=2}, {1+1/(x-2), 3>x>=2.1}}],{x,-2,3}]
        c) Plot[Piecewise[{{2+-2x, -5<=x<-0.1}, {1, 0.1>x>=-0.1}, {2+2x, 5>x>=0.1}}],{x,-5,5}]