**TI89**MAINAppVariable file 10/04/05, 11:07RdrvgrfnxÚĽZ€óGż§*7BJ Vríiäf   p Deriv GraphsSonya Land9/24/02v.2 by Bird afprime6If f'(a)=0, what three  possibilities could be true for f at x=a?Pf has a local max,  local min, or a flat place at x=a.PPderiv2tst1If f'(a)=0 and f"(a)>0,  what is true at x=a on f?Pf has a local min at x=aPYderiv2tst2If f'(a)=0 and f''(a)<0,  what is true about f at x=a?Pf has a local max at x=aPYderiv2tst3If f'(a)=0 and f''(a)=0,  what is true about f at x=a?PNothing can be concluded.PŔprimegr1 8V€(€ € €     P(€   € @     Ŕ@0P € @ € € 0 €  ` Ŕ @ ˙˙˙˙˙˙˙˙˙˙ű(€ $# č   €         €(      @  ŔA0@  _Given f' _above, _what is &_true about /_f"?Pf" is positive on (-inf,- 1.2)and (.5, inf) since f' is increasing;&f" is negative on (-1.2, /.5) since f' is 8decreasing; Af"=0 at x=-1.2 and x=.5Pżprimegr2 8V€(€ € €     P(€   € @     Ŕ@0P€ @ € € 0 €  ` Ŕ @˙˙˙˙˙˙˙˙˙˙ř(€ $# č   €         €( @ ŔA0@ _Given f' _above, _what is &_true about /_f?Pf is increasing on (-2,0)  and (1, inf) since f'>0;f is decreasing on (-inf,-2) and (0,1) since f'<0;&f has a local max at x=0 /and local mins at x=-2 and 8x=1P]thought 1If f'(x)=Ax+B, what type  of graph will f(x) be? Why?Pf(x) will be a quadratic  function of the formAx^2+Bx +C. If A>0, then f' is always increasing, &and f is always concave /up. No changes in 8concavity result in a Aparabola shape.PQthought 2If f'(x)=Ax+B, what type  of graph will f" be? Why?Pf"(x)=A since the slope of  f' or f" is A. f" will be a constant function or a horizontal line at y=A.PŔprime2gr1 8V€(€ € €     P(€   € @     Ŕ@0P € @ € € 0 €  ` Ŕ @ ˙˙˙˙˙˙˙˙˙˙ű(€ $# č   €         €(      @  ŔA0@  _Given f" _above, _what is&_true about /_f'?PĎf' is increasing on (-2,0)  and (1, inf) since f''>0;f 'is decreasing on (-inf,-2) and (0,1) since &f''<0;/f' has a local max at x=0 8and local mins at x=-2 and Ax=1PPŔprime2gr2 8V€(€ € €     P(€   € @     Ŕ@0P€ @ € € 0 €  ` Ŕ @˙˙˙˙˙˙˙˙˙˙ř(€ $# č   €         €( @ ŔA0@ _Given f" _above, _what is &_true about /_f?Pf is concave up on (-2,0)  and (1,inf) since f">0;f is concave down on (-inf,-2) and (0, 1) since &f"<0;/f has inflection pts at 8x=-2, 0 and 1PSTDYřBś