Question

Solution

Correct option is

decreasing on [0, )

                       

            

                      

Since log function is an increasing function and e < π,

log (e + x) < log (π + x). Thus (e + x) log (e + x) < (e + x)

log (π + x) < (π + x) log (π + x) for all x > 0.

Thus,f’ (x) < 0 for ∀ x > 0 ⇒ f (x) decreases on (0, ∞) 

SIMILAR QUESTIONS

Q1

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

Q2

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

 

Q3

If ab > 0 then the minimum value of  

Q4

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

Q5

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

Q6

The tangent to the curve 

At the point corresponding to  is

Q7

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

Q8

 the in this interval

Q9

The set of all values of a for which the function

                   

decreases for all real x is

Q10

The length of a longest interval in which the function 3 sin x – 4Sin3x is increasing is