ntIf f(x) be q polynomial of degree 4, such that f(0)=0, f(-1)=55 and f(x) has the points of relative maximum or relative minimum at x=1,2,3 thenn ntA) f(x) has two points of relative minima and one point of relative Maxima.n ntB) range of f(x) contains 9 negative integersn ntC) sum of real roots of f(x)=0 is 4n ntD) f(x) has exactly one inflection point.n ntn nt(One or more than one options correct type)n

Open in App

Solution

Suggest Corrections

Similar questions

Q. Let

f (x)

be a twice differentiable function and has no critical point and

g (x) = (x + 6)^{2009} (x + 1)^{2010} (x + 2)^{2011} (x - 3)^{2012} (x - 4)^{2013} (x - 5)^{2014}

be such that

f (x) + g (x) f^{^{'}} (x) + f^{''} (x) = 0

then function

h (x) = f^{2} (x) + (f^{^{'}} (x))^{2}

Q. Let

f (x)

be a twice differentiable function and has no critical points. Let

g (x) = (x + 6)^{2009} (x + 1)^{2010} (x + 2)^{2011} (x - 3)^{2012} (x - 4)^{2013} (x - 5)^{2014}

be such that

f (x) + g (x) f^{'} (x) + f^{''} (x) = 0.

Then the function

h (x) = f^{2} (x) + (f^{'} (x))^{2}

Q. Consider a real valued function

f : R \to R

satisfying

f (\frac{2 x + 3 y}{5}) = \frac{2 f (x) + 3 f (y)}{5} \forall x, y \in R

and

f (0) = 2; f^{'} (0) = 1

Minimum distance of a point on graph of

y = f (x)

from origin is less than or equal to

If $f_{1} (x) = x^{2} + 11 x + n$ and $f_{2} (x) = x$ , then the largest positive integer n for which the equation $f_{1} (x) = f_{2} (x)$ has two distinct real roots, is___

Q. A function f(x, y) is defined for non - negative integers
I. f(0, 0) = 0
II. f(2x, 2y) = f(2x + 1, 2y + 1) = f(x, y)
III. f(2x + 1, 2y) = f(2x, 2y + 1) = f(x, y) + 1
What is the value of f(11, 5)?

Join BYJU'S Learning Program