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the In This Interval

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Question

Solution

Correct option is

f (x) is an increasing function

Let u(x) = sinx – x cosx, so that u’(x) = x sinx > 0 for 0 < x ≤ 1. So u(x) > u(0) = 0. So ’(x) > 0 for 0 < x ≤ 1. Hence f  increases on (0, 1]. Let v(x) = tanx – x sec2x, so that v’(x) = –2x sec2x tanx < 0

for 0 < x ≤ 1. Thus v(x) < v(0), i.e., g’(x) < 0 for 0 < x ≤ 1. So g decreases on (0, 1].

SIMILAR QUESTIONS

Q1

The coordinates of the point P on the curve y2 = 2x3, the tangent at which is perpendicular to the line 4x – 3y + 2 = 0, are given by

Q2

The coordinates of points P(xy) lying in the first quadrant on the ellipsex2/8 + y2/18 = 1 so that the area of the triangle formed by the tangent at Pand the coordinate axes is the smallest, are given by

Q3

The points(s) on the curve y3 + 3x2 = 12y where the tangent is vertical is(are)

Q4

The equation of the common tangent to the curves y2 = 8x and xy = –1 is

Q5

If ab > 0 then the minimum value of

Q6

The curve y = ax3 + bx2 + cx + 8 touches x – axis at P(2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively

Q7

If the tangent at (1, 1) on y2 = x(2 – x)2 meets the curve again at P, is

Q8

The tangent to the curve

At the point corresponding to  is

Q9

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are

Q10

The set of all values of a for which the function

decreases for all real x is