Question 1156158


solve {{{f}}}´{{{(2)}}}  if {{{f(x) = x^3 - 6x^2 + 9x + 3}}}

{{{f}}}´{{{(x) = 3x^2 - 12x + 9}}}

{{{f}}}´{{{(2) = 3*2^2 - 12*2 + 9}}}

{{{f}}}´{{{(2) = 12 - 24 + 9}}}

{{{f}}}´{{{(2) = 21 - 24 }}}

{{{f}}}´{{{(2) =  - 3}}}


Determine the largest and smallest value of the function in the interval {{{0 <= x <= 5 }}}with derivatives.

Check for local minimums or maximums by setting {{{f}}}'{{{(x)}}} equal to {{{0}}}.

{{{0 = 3x^2 -12x + 9}}}........simplify, both sides divide by {{{3}}}

{{{0 = x^2-4x + 3}}}....factor

{{{0 = (x -1) (x -3)}}}

{{{x = 1}}} or {{{x=3}}}

Evaluate {{{f(x)}}} at the critical values, and at the end points.

{{{f(0) = 3}}}

{{{f(1) = 7}}}

{{{f(3) = 3}}}

{{{f(5) = 23}}}

{{{f(x)}}} has a minimum of {{{3 }}}and a maximum of {{{23}}}.