Find the slope of the curve at the indicated point. Let us consider the curve as x² + y³ = 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 x² + y³ = 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 x² + y³ = 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 x² + y³ = 4 we get,

2x + 3y² dy/dx = 0

⇒ dy/dx = -2x/3y²

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 x² + y³ = 4 is -4/75 at (2, 5)