What are the critical values, if any, of $f(x)=x^3 + 6x^2 − 15x$ ?

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Answer 1 · 2016-02-21T14:21:00

I have found all the value for $x$ but left the finishing off for the question proposer

Tony B

$color(green)("To find the x-axis intercepts")$

Factorizing: $" " x(x^2+6x-15)=0" "->" "color(blue)(x=0" is one solution")$

$x=(-b+-sqrt(b^2-4ac))/(2a)" "->" "(-6+-sqrt(36-4(1)(-15)))/(2(1))$

$x=(-6+-sqrt(96))/2" "=" " (-6+-4sqrt(6))/2$

$x= -3+-2sqrt(6)$

$color(blue)(=> x=-7.899" to 3 decimal places")$

$color(blue)(=> x=+1.899" to 3 decimal places")$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(green)("To find the Max/min")$

$f'(x)= 3x^2+12x-15=0$

$x=(-12+-sqrt(144-4(3)(-15)))/(2(3))$

$x=-12/6 +-sqrt(324/36)$

It is sometimes useful to take something inside the root as $sqrt(324/36) = sqrt(9)$

$x=-2+-3$

$color(blue)("Max/Min at " x=-5 " and " x=1)$

$color(green)("I will let you finish this off")$

What are the critical values, if any, of f(x)=x^3 + 6x^2 − 15x f(x)=x^3 + 6x^2 − 15x?