How do you find the slope of the tangent to the curve #y = 1/sqrtx# at the point where x = a?

Answer 1

You can find the derivative and evaluate it at your point:

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Answer 2

To find the slope of the tangent to the curve (y = \frac{1}{\sqrt{x}}) at the point where (x = a), you use differentiation to find the derivative of (y) with respect to (x), which gives the slope of the tangent line at any point (x) on the curve.

Given (y = \frac{1}{\sqrt{x}}), we can rewrite (y) as (x^{-\frac{1}{2}}).

The derivative of (y) with respect to (x), denoted as (\frac{dy}{dx}) or (y'), is found using the power rule for differentiation. The power rule states that if (y = x^n), then (y' = nx^{n-1}).

Applying this rule to (y = x^{-\frac{1}{2}}), we get:

[y' = -\frac{1}{2}x^{-\frac{1}{2} - 1} = -\frac{1}{2}x^{-\frac{3}{2}}]

This derivative gives us the slope of the tangent at any point (x) on the curve. To find the slope at (x = a), substitute (x) with (a):

[y' = -\frac{1}{2}a^{-\frac{3}{2}}]

Therefore, the slope of the tangent to the curve (y = \frac{1}{\sqrt{x}}) at the point where (x = a) is (-\frac{1}{2}a^{-\frac{3}{2}}).

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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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