The global maximum value of f(x)=(log)(1...

The global maximum value of `f(x)=(log)_(10)(4x^3-12 x^2+11 x-3),x in [2,3],` is `-3/2(log)_(10)3` (b) `1+(log)_(10)3` `(log)_(10)3` (d) `3/2(log)_(10)3`

`(-3)/2log_(10)3`

`1+log_(10)3`

`log_(10)3`

`3/2log_(10)3`

Text Solution

Verified by Experts

The correct Answer is:

Let `g(x)=4x^(3)-12x^(2)+11x-3`
`:.g^(')(x)=10x^(2)-24x+11`
`=12(x-1)^(2)-1gt0` for `0epsilon [2,3]`
`f(x)_(max)=f(3)=log_(1)(4xx27-12xx9-11xx3-3)`
`=log_(10)30=1+log_(10)3`

Topper's Solved these Questions

TEST PAPERS
RESONANCE ENGLISH|Exercise Math|105 Videos
TEST PAPER
RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos
TEST SERIES
RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

In a binomial distribution B(n , p=1/4) , if the probability of at least one success is greater than or equal to 9/(10) , then n is greater than (1) 1/((log)_(10)^4-(log)_(10)^3) (2) 1/((log)_(10)^4+(log)_(10)^3) (3) 9/((log)_(10)^4-(log)_(10)^3) (4) 4/((log)_(10)^4-(log)_(10)^3)

The equation (log_10x+2)^3+(log_10x-1)^3=(2log_10x+1)^3 has

[log_10⁡(x)]^2 − log_10⁡(x^3) + 2=0

Which of the following pairs of expression are defined for the same set of values of x ? f_1(x)=2(log)_2xa n df_2(x)=(log)_(10)x^2 f_1(x)=(log)x_xx^2a n df_2(x)=2 f_1(x)=(log)_(10)(x-2)+(log)_(10)(x-3)a n df_(2(x))=(log)_(10)(x-2)(x-3)dot

Which of the following pairs of expression are defined for the same set of values of x ? f_1(x)=2(log)_2xa n df_2(x)=(log)_(10)x^2 f_1(x)=(log)_xx^2a n df_2(x)=2 f_1(x)=(log)_(10)(x-2)+(log)_(10)(x-3)a n df_(2(x))=(log)_(10)(x-2)(x-3)dot

Solve (x^(log_(10)3))^(2) - (3^(log_(10)x)) - 2 = 0 .

Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2^y=2. Then - (a) . x=(log)_(10)5\ a n d\ y=(log)_(10)2 (b) . x=(log)_(10)2\ a n d\ y=(log)_(10)5 (c) . x=(log)_(10)(1/5)\ a n d\ y=(log)_(10)2 (d) . x=(log)_(10)5\ a n d\ y=(log)_(10)(1/2)

If (1)/("log"_(x)10) = (2)/("log"_(a)10)-2 , then x =

Find x, if : (i) log_(10) (x + 5) = 1 (ii) log_(10) (x + 1) + log_(10) (x - 1) = log_(10) 11 + 2 log_(10) 3

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS

The derivative of y = (1-x) (2-x)…(n-x) at x= 1 is
Text Solution
|
If f(x)=|sinx-|cosx||, then the value of f^(')(x) at x=(7pi)/6 is
Text Solution
|
The global maximum value of f(x)=(log)(10)(4x^3-12 x^2+11 x-3),x in [2...
Text Solution
|
If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have no...
Text Solution
|
If 3f(cosx)+2f(sinx)=5x, then f^(')(cosx) is equal to (where f^(') den...
Text Solution
|
"If "y=x^((x^(x)))," then "(dy)/(dx) is
Text Solution
|
If f (x)=(4+x )^(n), n in N and f'(0) represents then r^(th) derivativ...
Text Solution
|
Let f(x)=x/(1+x^2) and g(x)=(e^(-x))/(1+[x]) (where [.] denote greates...
Text Solution
|
If the derivative of an odd cubic polynomial vanishes at two different...
Text Solution
|
f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...
Text Solution
|
Find the critical (stationary ) points of the function f(X)=(x^(5))/(2...
Text Solution
|
If curve y=1-ax^(2) and y=x^(2) intersect orthogonally then a is
Text Solution
|
If the relation between subnormal SN and subtangent ST on the curve, b...
Text Solution
|
Find the point on the curve y=x^3-11 x+5 at which the tangent is y"...
Text Solution
|
Find the equation of tangent to the hyperbola 16x^(2)-25y^(2)=400 perp...
Text Solution
|
Find the rate of change of volume of a sphere with respect to its s...
Text Solution
|
((2x+3y)/5)+(2f(x)+3f(y))/5 and f^(')(0)=p and f(0)=q. Then f^(")(0) i...
Text Solution
|
If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...
Text Solution
|
If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...
Text Solution
|
The curve y=2e^(2x) intersect the y-axis at an angle cot^(-1)|(8n-4)/3...
Text Solution
|