Q. 145.0( 8 Votes )

If tangent to the

Answer :

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,



OR


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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