Answer :

**Given:** Tangent to the curve y^{2} + 3x – 7 = 0 at point (h, k) is parallel to line x – y = 4

**To Find:** Value of k

Differentiating the curve with respect to x we get,

⇒

⇒

At point (h, k),

⇒

And the line is parallel to the line x – y = 4

⇒ Slope of the line is = 1

So, equating both the slopes we get,

⇒

**OR**

**Given:** y = 5x – 2x^{3} and x increases at the rate of 2units/sec

**To Find:** Rate of change of curve at x = 3.

Slope of the curve is,

Rate of change of slope is =

Rate of change of x is = units/sec

So, at x = 3, the rate of change of slope is (-12 x 3 x 2) = -72 units/sec.

That means the slope is decreasing at the rate of 72 units/sec.

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