L e tf(x)={|x^2-3x|+a ,0lt=x<3/2 -2x+3,...

`L e tf(x)={|x^2-3x|+a ,0lt=x<3/2 -2x+3,xgeq3/2` If `f(x)` has a local maxima at `x=3/2` , then greatest value of `|4a|` is _________

Text Solution

Verified by Experts

The correct Answer is:

-2.25

`f(3/2)=0underset(xrarr3/2)lim|x^(2)-3x|+ale0 or ale-9/4`
Hence greatest value of a is -2.25

Topper's Solved these Questions

MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Single Correct Answer Type|13 Videos
MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos
MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Matrix Match Type|11 Videos
METHODS OF DIFFERENTIATION
CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos
MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS
CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={|x^2-3x|+a ,0lt=x<3/2 -2x+3,xgeq3/2 If f(x) has a local maxima at x=3/2 , then greatest value of |4a| is _________

L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

If f(x)=max{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x > 0 f(x) = { 1/(64), 0 lt= x lt = 1/4 x^2, 1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

Discuss the continuity of f(x)={(x{x}+1 ,, 0lt=x<1),(2-{x} ,, 1lt=x<2):} where {x} denotes the fractional part function.

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____

If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 ;0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 ;0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Let f(x)={(sinx+cosx",",0 lt x lt (pi)/(2)),(a",",x=pi//2),(tan^(2)x+"cosec"x",",pi//2 lt x lt pi):} Then its odd extension is

Find the equivalent definition of f(x)=max{x^2,(1-x)^2,2x(1-x)} where 0lt=xlt=1

Let f(x)=x^3-3x^2+6AAx in \mathbb{R} and g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq

CENGAGE PUBLICATION-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Numerical Value Type

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1...
Text Solution
|
If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when x and y are s...
Text Solution
|
For a cubic function y=f(x),f^(x)=4x at each point (x , y) on it and i...
Text Solution
|
Number of integral values of b for which the equation (x^3)/3-x=b has ...
Text Solution
|
L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1 Then number of times f^(...
Text Solution
|
The number of nonzero integral values of a for which the function f(x)...
Text Solution
|
L egf(x)={x^(3/5),ifxlt=1-(x-2)^3,ifx >1 Then the number of critical ...
Text Solution
|
A right triangle is drawn in a semicircle of radius 1/2 with one of...
Text Solution
|
A rectangle with one side lying along the x-axis is to be inscribed in...
Text Solution
|
The least integral value of x where f(x)=(log)(1/2)(x^2-2x-3) is monot...
Text Solution
|
The least area of a circle circumscribing any right triangle of area 9...
Text Solution
|
L e tf(x)={|x^2-3x|+a ,0lt=x<3/2 -2x+3,xgeq3/2 If f(x) has a local m...
Text Solution
|
Let f(x)=30-2x -x^3, the number of the positive integral values of x w...
Text Solution
|
Let f(x) ={{:(x(x-1)(x-2),(0lexltn),sin(pix),(nlexle2n):} least valu...
Text Solution
|
Number of critical point of the function f(X) =x+sqrt(|x|) is .
Text Solution
|
consider f(X) =(1)/(1+|x|)+(1)/(1+|x-1|) Let x(1) and x(2) be point wh...
Text Solution
|
Let f be a function defined on R (the set of all real numbers) such th...
Text Solution
|
Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...
Text Solution
|
Let p(x) be a real polynomial of least degree which has a local maximu...
Text Solution
|
A cylindrical container is to be made from certain solid material with...
Text Solution
|