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How do you find the critical points for #f(x)=-x^2+6x+2#?

Answer 1

Isabella Ackerman

#x=3#

Given polynomial function:

#f(x)=-x^2+6x+2#

#f'(x)=-2x+6#

#f''(x)=-2#

for critical (minima or maxima) points #f'(x)=0#, hence

#-2x+6=0#

#x=6/2#

#x=3#

since #f''(x)=-2<0# hence the function is maximum at #x=3#

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Answer 2

Luke Alvarez

To find the critical points of ( f(x) = -x^2 + 6x + 2 ), you need to find the values of ( x ) where the derivative of ( f(x) ) is equal to zero or undefined. First, find the derivative of ( f(x) ) with respect to ( x ) using the power rule:

( f'(x) = -2x + 6 )

Now, set ( f'(x) ) equal to zero and solve for ( x ):

( -2x + 6 = 0 )

( -2x = -6 )

( x = 3 )

So, the critical point of ( f(x) ) is ( x = 3 ).

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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.