A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve y2 = 4x + 5. Then, the point of contact is
(2, 1)
(- 1, 1)
(1, 3)
(3, 4)
B.
(- 1, 1)
Given equation of curve is y2 = 4x + 5.
On differentiating both sides w.r.t. x, we get
Also, given straight line is 2x - y + 5 = 0.
So, the slope of this line is m, = 2
Since, the line is parallel to the tangent of the curve.
Hence, the point of contact is (- 1 1).
The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm, then the rate of decreasing of its height is
6 cm/min
3 cm/min
4 cm/min
5 cm/min
The function is not suitable to apply Rolle's theorem, since
f(x) is not continuous on [1, 5]
f(1) f(5)
f(x) is continuous only at x = 4
f(x) is not differentiable at x = 4