Is #f(x)=x^2-3lnx# increasing or decreasing at #x=1#?

Answer 1

The function #f(x)# is decreasing

The domain of #f(x)# is for #x>0# because of #lnx#

We must compute the function's derivative in order to ascertain whether a function is increasing or decreasing.

Here #f(x)=x^2-3lnx#
So the derivative is #f'(x)=(x^2)'- (lnx)'=2x-3/x#
Then we calculate #f'(1)=2-3=-1#
Therefore #f(x)# is decreasing at #x=1#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To determine whether ( f(x) = x^2 - 3 \ln(x) ) is increasing or decreasing at ( x = 1 ), we need to check the sign of the derivative of ( f(x) ) at ( x = 1 ).

The derivative of ( f(x) ) is ( f'(x) = 2x - \frac{3}{x} ).

At ( x = 1 ), ( f'(1) = 2(1) - \frac{3}{1} = 2 - 3 = -1 ).

Since the derivative is negative at ( x = 1 ), the function ( f(x) = x^2 - 3 \ln(x) ) is decreasing at ( x = 1 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7