Other for Mar 12, 2009

Review: Section 3.3, 3.4, 4.3, 4.5 ? d/dx ln(x)= 1/x (1) ? d/dx ex= ex (1) ? lne=1 ? ln1=0 ? ln0=undefined ? e0=1 ? e1=e ? natural logarithm form: y=lnx ? exponential form: ey=x ? The base a: logax=b ab=x Ex: log28=3 23=8 ? change of base formula: logax= lnx/lna Ex: log23= ln3/ln2=1.585 ? To bring an exponent down, simple ln both sides: Ex: y=xx lny=lnxx lny=xlnx ? Algebra Review: x2x3=x5 (x2)3=x6 3x3y=9x+y exey=ex+y ex/ey=ex-y ln(xy)=lnx+lny ln(x/y)=lnx-lny lnxc=clnx ? slope of the tangent line=the derivative of the function ? equation of the tangent line: y-y1=m(x-x1) ? To find relative extrema: 1.) find the derivative 2.) set derivative=0 3.) use number line to find +/- ? +/-=relative minimum ? -/+=relative maximum ? concavity=the second derivative ? A point of inflection is the change in concavity ? concave up f"(x)>0 ? concave down f"(x)<0 ? f is increasing f'(x)>0 ? f is decreasing f'(x)<0