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

Extrema

In hx = fx + ...

Question

In h(x) = f(x) + f(-x), then h (x) has got an extreme value at a point where f'(x) is

even function.

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

odd function.

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

zero

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

None of these

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

Open in App

Solution

The correct option is A
even function.

We have, h'(x) = f'(x) - f'(-x)
For extreme value of h(x), h'(x) = 0
$\Rightarrow$ f'(x) = f'(-x) $\Rightarrow$ f'(x) is an even function.

Suggest Corrections

Similar questions

In h(x) = f(x) + f(-x), then h (x) has got an extreme value at a point where f'(x) is

f (1) = 2

f^{'} (x) = f (x)

x \in R

h (x) = f (f (x))

h^{'} (1)

f (x)

3

f (- 1) = 10, f (1) = 6, f (x)

x = - 1

f^{'} (x)

x = 1

f (x)

x

f^{''} (x) = - f (x)

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

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

h (5) = 11

h (10)

f (x) = a log x + b x^{2} + x

x = - 1, x = 2

a = \dots . ., b = \dots \dots

Join BYJU'S Learning Program