{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "Geneva" 1 12 0 0 0 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 257 "Geneva" 1 18 0 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 258 "Geneva" 1 12 0 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "Geneva" 1 12 0 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "Geneva" 0 10 0 0 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "Geneva" 0 10 0 0 0 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 264 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "Geneva" 0 10 0 0 0 1 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Geneva" 1 10 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" 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(-1.0)^(1/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+++++]!#5$\"+QSD g')F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 85 "So we define a cube roo t function which gves the real cube root of a negative number." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "real_cube_root := x -> if evalf(x) \+ > 0 then evalf(x^(1/3)) else -(evalf((-x)^(1/3))) fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/real_cube_rootGf*6#%\"xG6\"6$%)operatorG%&arrow GF(@%2\"\"!-%&evalfG6#9$-F06#*$)F2#\"\"\"\"\"$F8,$-F06#*$),$F2!\"\"F7F 8F@F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "real_cube_root (-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f := (x,y) -> real_cube_root(x^3-3*x*y^2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operat orG%&arrowGF)-%/real_cube_rootG6#,&*$)9$\"\"$\"\"\"F5*(F4F5F3F5)9%\"\" #F5!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot3d(f, -.1.. .1,-.1.. .1,shading=zhue);" }}{PARA 13 "" 1 "" {GLPLOT3D 328 176 176 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tan^2(theta))^(1/3), so the dire ctional derivative in the direction v\n is cos(theta) *(1- 3 * \+ tan^2(theta))^(1/3) rather than cos(theta).\n Thus f is not diffe rentiable at (0,0).\n" }}}}}{MARK "1 0 0" 24 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }