MyQuestionIcon

1

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

Theorems on Integration

If the functi...

Question

If the function f(x)= x³-3ax²+b is strictly increasing derivative for x > 0, then which of the following is always true?

A

a can take any real value

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

B

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

C

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

D

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

Open in App

Solution

The correct option is D
f(x) = x³ -3ax² + b

f'(x) = 3x² - 6ax

for f(x) to be increasing f'(x) > 0.

3x² - 6ax > 0

3x (x - 2a) > 0

(x - 2a) > 0 [There fore x > 0]

x > 2a

So, a ≥0

Suggest Corrections

thumbs-up

0

Similar questions

If the function f(x)= x³-3ax²+b is strictly increasing derivative for x > 0, then which of the following is always true?

Q. Without using the derivative, show that the function f (x) = | x | is
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0).

f : [0, \infty) \to R

be a strictly increasing function such that the functions

g (x) = f (x) - 3 x

h (x) = f (x) - x^{3}

are both strictly increasing function. Then the function

F (x) = f (x) - x^{2} - x

f (x)

is a differentiable function and

f (x) - x^{3}

is strictly increasing, then

f (x) + x - x^{2}

Q. Determine for what values of

x

f (x) = x^{3} + \frac{1}{x^{3}} (x \neq 0)

is strictly increasing or strictly decreasing.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Theorems on Integration

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorems on Integration

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon