# How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for # f(x) = sqrt(x^2+1) #?

If

# { (x<0, => f'(x)<0, =>, "strictly decreasing"), (x=0, => f'(x)=0, =>, "stationary"), (x>0, => f'(x)>0, =>, "strictly increasing") :} #

minimum at

graph{sqrt(x^2+1) [-10, 10, -5, 5]}

We can deduce from the graph that

f(x) is # { ("strictly decreasing", x<0), ("stationary", x=0), ("strictly increasing", x>0) :} #

So let's prove this using calculus.

Which concludes the deduction

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

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.

- How do you find the intervals of increasing and decreasing given #y=(3x^2-3)/x^3#?
- How do you find the maximum value of # y = -x^2 + 8x - 4#?
- Is #f(x)=4x-e^(3x-2) # increasing or decreasing at #x=-2 #?
- How do you determine if rolles theorem can be applied to # f(x) = sin 2x# on the interval [0, (pi/2)] and if so how do you find all the values of c in the interval for which f'(c)=0?
- How do you find the absolute maximum and absolute minimum values of f on the given interval: #f(t) =t sqrt(25-t^2)# on [-1, 5]?

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