Find all x-value(s) where #f(x) = 3^2-2/3+1# has a horizontal tangent line?

Find the derivatives f' (x) of the function f (x)

Answer 1

Any x-value

#f(x)# is just a constant. The derivative of any constant is #0#. So:
#f'(x)=0#.

So any x-value has a horizontal tangent line.

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Answer 2

To find the x-values where f(x) has a horizontal tangent line, we need to find the values of x where the derivative of f(x) is equal to zero. The derivative of f(x) can be found by taking the derivative of each term separately.

The derivative of 3^2 is 0, as it is a constant. The derivative of -2/3 is 0, as it is also a constant. The derivative of 1 is 0, as it is a constant.

Therefore, the derivative of f(x) is equal to zero for all values of x.

In conclusion, f(x) has a horizontal tangent line for all values of x.

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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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