How do you find the critical numbers of #f(x)=(x^2+6x7)^2#?
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To find the critical numbers of ( f(x) = (x^2 + 6x  7)^2 ), you first find the derivative of the function and then solve for values of ( x ) where the derivative equals zero or is undefined.

Find the derivative of ( f(x) ) using the chain rule and power rule: [ f'(x) = 2(x^2 + 6x  7)(2x + 6) ]

Set the derivative equal to zero and solve for ( x ): [ 2(x^2 + 6x  7)(2x + 6) = 0 ] [ (x^2 + 6x  7)(2x + 6) = 0 ]

Solve each factor for zero: [ x^2 + 6x  7 = 0 ] and [ 2x + 6 = 0 ]

Solve the quadratic equation ( x^2 + 6x  7 = 0 ) using the quadratic formula or factoring.

Solve ( 2x + 6 = 0 ) for ( x ).

The values of ( x ) obtained from steps 4 and 5 are the critical numbers of the function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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