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The maximum slope of the curve $y=-x^3 + 3x^2 + 9x-27$ is: |
0 12 16 32 |
12 |
$y=-x^3 + 3x^2 + 9x-27$ function of maximise = $y'=-3x^2+6x+9=g(x)$ $g(x)=-3(x^2-2x-3)$ $g'(x)=-6x+6=0⇒ x = 1$ $g''(x)=-6⇒(g''(1)=6)<0$ ⇒ x = 1 point of maxima $g(max)=-3(1-2-3)=12$ |
