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# Find the slope of the curve at the indicated point. Let us consider the curve as x^{2} + y^{3} = 4 and the indicated point is (2, 5).

We will use the concept of differentiation to find the slope of the curve.

## Answer: The slope of the curve x^{2} + y^{3} = 4 is -4/75 at the indicated point (2, 5)

Let us see how we will use the concept of differentiation to find the slope of the curve.

**Explanation**:

We have been given the curve x^{2} + y^{3} = 4. In order to find the slope of the curve, we have to find the derivative dy/dx for the curve and then substitute the point (2, 5) in the expression of dy/dx.

Let us find dy/dx.

On differentiating both sides of the curve x^{2} + y^{3} = 4 we get,

2x + 3y^{2} dy/dx = 0

⇒ dy/dx = -2x/3y^{2}

On substituting x = 2 and y = 5 in the above expression we get,

dy/dx = (-2 × 2) / (3 × 5 × 5) = -4/75

### Thus, the slope of the curve x^{2} + y^{3} = 4 is -4/75 at (2, 5)

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