What are the values and types of the critical points, if any, of #f(x) =x^3 + 3x^2-24x#?

Answer 1

#(2, -28)# Minimum Point,
#(-4, 80)# Maximum Point and #(-1, 26)# Point of inflection

#f(x)=x^3+3x^2-24x# the given #f' (x)=3 x^2 +6 x-24# the first derivative
Let #f' (x) = 0# #3 x^2 +6 x-24=0# solving for x: #x=2# and #x=-4# when #x=2# , #y=-28# Minimum point when #x=-4#, #y=80# Maximum Point
Solving for #f'' (x)# #f'' (x)=6x+6# set #f''(x)=0# and solving for x: #6x+6=0# #x=-1# when #x=-1#, #y=26# Point of inflection
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Answer 2

The critical points of ( f(x) = x^3 + 3x^2 - 24x ) are at ( x = -6, x = 0, ) and ( x = 4 ). The corresponding values of the critical points are ( f(-6) = -216, f(0) = 0, ) and ( f(4) = 32 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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