Let f x be a differentiable function on -0-8- such that f 1-6- f 2-1-3- f 3-8- f 4-2- f 5-5- f 6-1-5- and f 7-1-3 Ifthe minimum number of roots of the equation f - x - f - x f x 2-0 is - then -11 i

f'(x) = 0, f(x) = 1, f(x) = 1 f'(x) = 0 for atleast 4 points nbsp; f(x) = 1 for atleast 5 points f(x) = 1 for atleast 2 points So f'(x) = f'(x) f^2(x) = 0 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Extrema

Let f x be a ...

Question

Let $f (x)$ be a differentiable function on $[0, 8]$ such that $f (1) = 6, f (2) = \frac{1}{3}, f (3) = 8, f (4) = - 2, f (5) = 5, f (6) = \frac{1}{5}, and f (7) = - \frac{1}{3}$ If the minimum number of roots of the equation $f^{'} (x) - f^{'} (x) (f (x))^{2} = 0 is λ then \frac{λ}{11}$ is

Open in App

Solution

$f^{'} (x) = 0, f (x) = 1, f (x) = - 1$
$f^{'} (x) = 0$ for atleast 4 points
$f (x) = 1$ for atleast 5 points
$f (x) = - 1$ for atleast 2 points
So $f^{'} (x) = f^{'} (x) f^{2} (x) = 0$ has atleast 11 roots.
So $\frac{λ}{11} = \frac{11}{11} = 1$

Suggest Corrections

Similar questions

Q. Let

f (x)

be a differentiable function on

[0, 8]

such that

f (1) = 6, f (2) = \frac{1}{3}, f (3) = 8, f (4) = - 2, f (5) = 5, f (6) = \frac{1}{5}, and f (7) = - \frac{1}{3}

If the minimum number of roots of the equation

f^{'} (x) - f^{'} (x) (f (x))^{2} = 0 is λ then \frac{λ}{11}

Let f(x) be cubic polynomial such that f(1)=1, f(2)=2, f(3)=3 and f(4)=16. Find the value of f(5).

Suppose f (x) is a polynomial of degree 5 and with leading coefficient 2009. Suppose further that f (1)=1, f (2)=3,f (3)=5,f (4)=7,f (5)=9. What is the value of f (6).

Q. Let N be the set of natural numbers, Define a real valued function

f : N \to N

f (x) = 2 x + 1

.
Using this definition, complete the table given below.

x	1	2	3	4	5	6	7
y	f(1)=	f(2)=	f(3)=	f(4)=	f(5)=	f(6)=	f(7)=

Q. Let

f (x)

be an even function & even degree polynomial such that

f (\begin{matrix} \frac{1}{2} \end{matrix}) = \frac{1}{2}, f (1) = 1, f (2) = - 3, f (3) = 5

then minimum number of points of intersection for

f (x)

Join BYJU'S Learning Program

Let f(x) be a differentiable function on [0,8] such that f(1)=6,f(2)=13,f(3)=8,f(4)=−2,f(5)=5,f(6)=15, and f(7)=−13 If the minimum number of roots of the equation f′(x)−f′(x)(f(x))2=0 is λ then λ11 is

f′(x)=0,f(x)=1,f(x)=−1 f′(x)=0 for atleast 4 points f(x)=1 for atleast 5 points f(x)=−1 for atleast 2 points So f′(x)=f′(x) f2(x)=0 has atleast 11 roots. So λ11=1111=1

Let $f (x)$ be a differentiable function on $[0, 8]$ such that $f (1) = 6, f (2) = \frac{1}{3}, f (3) = 8, f (4) = - 2, f (5) = 5, f (6) = \frac{1}{5}, and f (7) = - \frac{1}{3}$ If the minimum number of roots of the equation $f^{'} (x) - f^{'} (x) (f (x))^{2} = 0 is λ then \frac{λ}{11}$ is

$f^{'} (x) = 0, f (x) = 1, f (x) = - 1$
$f^{'} (x) = 0$ for atleast 4 points
$f (x) = 1$ for atleast 5 points
$f (x) = - 1$ for atleast 2 points
So $f^{'} (x) = f^{'} (x) f^{2} (x) = 0$ has atleast 11 roots.
So $\frac{λ}{11} = \frac{11}{11} = 1$