Home
Class 12
MATHS
Let f(x) be defined as f(x)={tan^(-1)alp...

Let `f(x)` be defined as `f(x)={tan^(-1)alpha-5x^2,0

Text Solution

Verified by Experts

The correct Answer is:
`alpha lt -tan 1`
`f(x)={{:(tan^(-1) alpha-5x^(2),0ltxlt),(-6x,xge1):}`
f(1)=-6
for maximum at x=1
`underset(xrarr1)lim f(x)=tan^(-1)alpha -5lt-6`
or `tan^(-1)alphalt-1 or alpha-tan 1`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.5|5 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.6|9 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.3|6 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a function defined as f(x)={{:(sin(x^2-3x)", "xle0),(6x+5x^2", "xgt0):} Then at x=0,f(x)

Let f : I - {-1,0,1} to [-pi, pi] be defined as f(x) = 2 tan^(-1) x - tan^(-1)((2x)/(1 -x^(2))) , then which of the following statements (s) is (are) correct ?

Let f:R rarr[0,(pi)/(2)) defined by f(x)=Tan^(-1)(x^(2)+x+a) then the set of values of a for which f is onto is

Let f :R-> R be defined by f(x)={(alpha+sin[x]/x,if x>0 ),(2,if x=0),(beta+[(sinx-x)/x^3],if x<0):} where [x] denotes the integral part of x. If f continuous at x = 0 , then beta-alpha =

Let f:R rarr [0, (pi)/(2)) be a function defined by f(x)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

Let f:R rarr R be defined by f(x)=2+alpha x,alpha!=0 , If f(x)=f^(-1)(x) , for all x in R , then alpha equals

Let f:R rarr(0,(2 pi)/(2)] defined as f(x)=cot^(-1)(x^(2)-4x+alpha) Then the smallest integral value of alpha such that,f(x) is into function is

Let f(x) be a function defined as below : f(x)=sin(x^(2)-3x) ,x le 0 =6x+5x^(2), x gt 0 then at x=0 ,f(x)

Let f:[0,2]rarr[2,5] be defined as f(x)=3x^(2)-6x+5, then f(x) is

Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( 3x^(2) + 6x + a)". If " f(x) is an onto function . then the value of a si