If $x_{0}$ is the x-coordinate of the point of inflection of curve $y = f (x)$ then (assume second derivative exists)

f (x_{0}) \neq 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f (x_{0}) = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f^{''} (x_{0}) = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

f^{''} (x_{0}) \neq 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $f^{''} (x_{0}) = 0$
If $x_{o}$ is the x-coordinate of the point of the inflection of curve $y = f (x)$ , then the second derivative of the function must be zero at the inflection point.
Because $f (x_{o} + h)$ and $f (x_{o} - h)$ are of opposite sign, which is the condition for inflection point.

$∴ f^{''} (x_{0}) = 0$

Suggest Corrections

Similar questions

For the expression f(x) = a $x^{2}$ + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value $x_{0}$ is

For the expression f(x) = a $x^{2}$ + bx + c (a < 0), $b^{2}$ > 4ac always. A real value $x_{0}$ will lie in between the real roots of f(x) if

Q. Let

f : R \to R

be a continuous decreasing function. A point

x_{0} \in R

is said to be a fixed point of

f

f (x_{0}) = x_{0} .

The number of fixed points of

f \circ f \circ f

equals

Q. If both f(x) and g(x) are differentiable functions at

x = x_{0}

, then the function defined as h(x) = maximum {f(x), g(x)} :

Q. Let f(x) and g(x) are defined and differentiable for

x \geq x_{0}

and

f (x_{0}) = g (x_{0}), f^{'} (x) > g^{'} (x)

for

x > x_{0}

then

Join BYJU'S Learning Program

If x0 is the x-coordinate of the point of inflection of curve y=f(x) then (assume second derivative exists)

If $x_{0}$ is the x-coordinate of the point of inflection of curve $y = f (x)$ then (assume second derivative exists)