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")#