Let p(x) be a real polynomial of least d...

Let `p(x)` be a real polynomial of least degree which has a local maximum at `x=1` and a local minimum at `x=3.` If `p(1)=6a n dp(3)=2,` then `p^(prime)(0)` is_____

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos
APPLICATIONS OF DERIVATIVES
TARGET PUBLICATION|Exercise CRITICAL THINKING|129 Videos
APPICATIONS OF DEFINITE INTEGRAL
TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos
BINOMIAL DISTRIBUTION
TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

Similar Questions

Explore conceptually related problems

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6 and p(3)=2, then p'(0) is

If P (x) be a polynomial of degree three that has a local maximum value 8 at x=1 and a local minimum value 4 at x=2 , then p (0 ) is equal to :

Let f(x) be a cubic polynomial which is having local maximum at (1,2) and f'(x) has local extrema at x=0 .If f(0)=1 then

Let g (x) be a cubic polnomial having local maximum at x=-1 and g '(x) has a local minimum at x =1, If g (-1) =10 g, (3) =- 22, then

Consider a polynomial P(x) of the least degree that has a maximum equal to 6 at x=1 and a minimum equal to 2 at x=3. Then the value of p(2)+P(0)-7 is

If P(x) is a polynomial of the least degree that has a maximum equal to 6 at x=1, and a minimum equalto 2 at x=3, then int_(0)^(1)P(x)dx equals:

Let P(x) be a real polynomial of degree 3 which vanishes at x=-3. Let P(x) have local minima at x=1, local maximum at x=-1 and underset(-1)overset(1)int P(x)dx=-18 , then the sum of all the coefficients of the polynomical P(x) is equal to........

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING

Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . ...
Text Solution
|
Let f,g and h be real-valued functions defined on the interval [0,1] b...
Text Solution
|
Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....
Text Solution
|
For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...
Text Solution
|
Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...
Text Solution
|
If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} an...
Text Solution
|
e total number of local maxima and local minima of the function f(x) =...
Text Solution
|
Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f ...
Text Solution
|
Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only re...
Text Solution
|
Let f be a function defined on R (the set of all real numbers) such th...
Text Solution
|
The points on the curve y=12x-x^3 at which the gradient is zero are
Text Solution
|
The displacement of a particle at time t is x, where x=t^4-kt^3. IF th...
Text Solution
|
If f(x) satifies of conditiohns of Rolle's theorem in [1,2] and f(x) i...
Text Solution
|
IF f(x)=x,-1lexle1, then function f(x) is
Text Solution
|
If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...
Text Solution
|
Let p(x) be a real polynomial of least degree which has a local maximu...
Text Solution
|
Let f(x) be a polynomial of degree four having extreme values at x=1 a...
Text Solution
|
if Agt0,Bgt0 and A+B=pi/3 then the maximum value of tanA.tanB is (A) 1...
Text Solution
|
A wire of length 2 units is cut into two parts which are bent respe...
Text Solution
|
Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...
Text Solution
|