If f(x) =x^(3)+bx^(2)+cx+d and 0lt b^(2)...

If `f(x) =x^(3)+bx^(2)+cx+d` and `0lt b^(2)ltc` then `in (-oo,oo)`

is strictly increasing

has a local maxima

has a local minima

has bounded area

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos
DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos
DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise Level -1|102 Videos
DIFFERENTIAL CALCULUS
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos
DIFFERENTIAL EQUATIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^3+bx^2+cx+d and 0< b^2 < c , then

For f(x)=x^(3)+bx^(2)+cx+d , if b^(2) gt 4c gt 0 and b, c, d in R , then f(x)

If f(x)={x^3,if x^2 =1 then f(x) is differentiable at (a) (-oo,oo)-{1} (b) (-oo,oo)-{1,-1} (c) (-oo,oo)-{1,-1,0} (d) (-oo,oo)-{-1}

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

If f(x)=(|x-1)/(x^2) the f(x) is one-one in (2,oo) b. one-one in (0,1) c. one-one in (-oo,0) d. one-one in (1,2)

Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true ?

The interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing is (a) ( -oo , oo ) (b) ( -oo , 0 ) (c) ( 2 , oo ) (d) ( 0 , 2 )

the interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing, is (a) ( -(oo) , (oo) ) (b) ( -(oo) , 0 ) (c) ( 2 , (oo) ) (d) ( 0 , 2 )

If the function f(x)=x^2-k x+5 is increasing on [2,\ 4] , then (a) k in (2,\ oo) (b) k in (-oo,\ 2) (c) k in (4,\ oo) (d) k in (-oo,\ 4)

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -2

For what values of a , the function f(x)={((sqrt(a+4))/(1-a))x^5-3x+"l...
Text Solution
|
If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...
Text Solution
|
If f(x) =x^(3)+bx^(2)+cx+d and 0lt b^(2)ltc then in (-oo,oo)
Text Solution
|
Let f(x) be a non-constant twice differentiable function defined on (-...
Text Solution
|
f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...
Text Solution
|
f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...
Text Solution
|
f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...
Text Solution
|
Given a function f:[0,4]toR is differentiable ,then prove that for som...
Text Solution
|
With the help of Lagrange's formula, prove that (a-b)/(a) le log (a/b)...
Text Solution
|
The function f(x)=int(0)^(x)sqrt(1-t^(4)) dt is such that
Text Solution
|
The function (sin(x+a))/(sin(x+b)) has no maxima or minima if
Text Solution
|
The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...
Text Solution
|
If f(x) is a cubic polynomial which has local maximum at x=-1,If f(2...
Text Solution
|
If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...
Text Solution
|
The maximum value of the function f(x)=3x^(3)-18x^(2)+27x-40 on the s...
Text Solution
|
If the function f(x)=x^(4)+bx^(2)+8x+1 has a horizontal tangent and a...
Text Solution
|
Let p(x) be a real polynomial of least degree which has a local maximu...
Text Solution
|
The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...
Text Solution
|
If the function f:[0,4]vecR is differentiable, the show that for a , b...
Text Solution
|
For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...
Text Solution
|