How do you find the local maximum and minimum values of # f(x) = 7x + 9x^(1)#?
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To find the local maximum and minimum values of ( f(x) = 7x + 9x^{1} ), you first need to find its critical points. Critical points occur where the derivative of the function is zero or undefined.

Find the derivative of ( f(x) ) with respect to ( x ): [ f'(x) = 7  9x^{2} ]

Set ( f'(x) = 0 ) to find critical points: [ 7  9x^{2} = 0 ] [ 7 = 9x^{2} ] [ x^{2} = \frac{7}{9} ] [ x = \pm \sqrt{\frac{9}{7}} ]

Check the second derivative to determine the nature of critical points: [ f''(x) = 18x^{3} ] At ( x = \sqrt{\frac{9}{7}} ), ( f''(x) ) is positive, indicating a local minimum. At ( x = \sqrt{\frac{9}{7}} ), ( f''(x) ) is negative, indicating a local maximum.

Evaluate the function at these critical points and endpoints if any exist to determine the local maximum and minimum values.
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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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