The Set Of All Values Of A For Which The Function Decreases For All Real x is

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

The set of all values of a for which the function

decreases for all real x is

medium

Solution

Correct option is

Differentiating, we get

For f (x) to be decreasing for all x, we must have f ‘(x) < 0 for all x.

This is possible only if

This inequality is always true if a > 1, i.e., a ∈ (1, ∞). Moreover, we must have a ≥ – 4 for to be real. Therefore, we have

[∴ we consider only a < 1]

⇒ a + 4 ≤ 1 + a² – 2a ⇒ 0 ≤ a² – 3a – 3

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

SIMILAR QUESTIONS

Q1

The coordinates of points P(x, y) 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

diffcult View solution

Q2

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

easy View solution

Q3

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

medium View solution

Q4

If a, b > 0 then the minimum value of

easy View solution

Q5

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

easy View solution

Q6

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

medium View solution

Q7

The tangent to the curve

At the point corresponding to is

easy View solution

Q8

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

easy View solution

Q9

the in this interval

easy View solution

Q10

medium View solution