# Is #f(x)=-e^(x^2+2) # increasing or decreasing at #x=0 #?

Find the first derivative, then evaluate at

So, at

hope that helped

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

To determine if ( f(x) = -e^{x^2+2} ) is increasing or decreasing at ( x = 0 ), we need to examine the sign of its derivative at that point.

The derivative of ( f(x) ) with respect to ( x ) is given by ( f'(x) = -2xe^{x^2+2} ).

Now, evaluate ( f'(0) ): [ f'(0) = -2(0)e^{0^2+2} = 0 ]

Since ( f'(0) = 0 ), we cannot determine the increasing or decreasing behavior of ( f(x) ) at ( x = 0 ) using the first derivative test. We may need to apply higher-order derivative tests or examine the function's behavior in the surrounding interval to determine its behavior more accurately.

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

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.

- Is #f(x)=(1-xe^x)/(1-x^2)# increasing or decreasing at #x=2#?
- What are the local extrema, if any, of #f (x) =x^2-2x+4#?
- What is the derivative graph of a parabola?
- Find the maxima and minima of function:- #y=2x^3-9x^2-24x+15#?
- Given the function #f(x)=x/(x+6)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [0,1] and find the c?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7