# 4.4 Formula Sheet (Final) - Formula sheet for Final Exam in...

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Formula sheet for Final Exam in Math 106 on Monday 14, 2007Derviative formulas(xp) =pxp-1(ex) =ex(lnx) =1xGeneral properties of derivatives(cf) =cf(f+g) =f+g(fg) =f g+f g(1/g) =-gg2(f/g) =f g-f gg2(f(g)) =f(g)gEquation to the tangent line to the graph atx0:y=f(x0) +f(x0)(x-x0)Exponentials.limn→∞(1 +1n)n=e= 2.71828. Properties:xpxq=xp+qexey=ex+y1/xp=x-p1/ex=e-x(xp)q=xpq(ex)y=exyh(t) =Aertsatisfiesh(t) =rh(t),h(0) =A. Ifr >0,t= (ln(2))/ris thedoubling time.Ifr <0,t= (ln(1/2))/ris thehalf-life.Natural Logarithm.By definitionelnx=x. This implies ln(ex) =x. Properties:ln(uv) = ln(u) + ln(v)ln(1/u) =-ln(u)ln(u/v) = ln(u)-ln(v)ln(up) =pln(u)Maxima and minima, increasing, decreasing, convex, concavefis increasing wheref(x)>0, decreasing wheref(x)<0.Iff(c) = 0 thencis a critical point.(This differs from the book, but is the commonlyaccepted definition). This is a necessary condition for the pointcto be a local maximum[minimum], i.e., there area < c < bso thatf(c) is the largest [smallest] value offon [a, b].

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