Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

How do you find the critical points of #h'(x)=x^2+8x-9#?

Answer 1

Emilia Aguilar

Critical points of # h^'(x) # are # x=-9 and x =1#

#h^' (x) = x^2+8 x-9 =0 # or

# (x+9)(x-1)=0 :. x+9=0 or x =-9 # and

# x-1=0 :. x=1 :. #

Critical points of # h^'(x) # are # x=-9 and x =1# [Ans]

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Answer 2

William Abdalla

To find the critical points of the function ( h'(x) = x^2 + 8x - 9 ), you need to first find its derivative, then set it equal to zero and solve for ( x ).

Find the derivative of ( h'(x) ) which is ( h''(x) = 2x + 8 ).
Set the derivative equal to zero: ( 2x + 8 = 0 ).
Solve for ( x ): ( 2x = -8 ), ( x = -4 ).

So, the critical point of ( h'(x) ) is ( x = -4 ).

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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.