Q. 145.0( 8 Votes )
If tangent to the
Given: Tangent to the curve y2 + 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,
Given: y = 5x – 2x3 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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