What does it mean if the first derivative is concave up?

A function f is concave up (or upwards) where the derivative f′ is increasing. This is equivalent to the derivative of f′ , which is f′′f, start superscript, prime, prime, end superscript, being positive. Graphically, a graph that’s concave up has a cup shape, ∪, and a graph that’s concave down has a cap shape, ∩.

How do you tell if graph is concave up or down?

In order to find what concavity it is changing from and to, you plug in numbers on either side of the inflection point. if the result is negative, the graph is concave down and if it is positive the graph is concave up.

What does the first derivative tell you about a graph?

The first derivative of a function is an expression which tells us the slope of a tangent line to the curve at any instant. Because of this definition, the first derivative of a function tells us much about the function. If is positive, then must be increasing. If is negative, then must be decreasing.

When is a function concave up?

A function is concave up if the second derivative is positive, and concave down when it is negative. A function looks “smiley” when it is concave up and “frowny” when it is concave down.

How do you find the second derivative?

The second derivative (f”), is the derivative of the derivative (f‘). In other words, in order to find a second derivative, take the derivative twice. One reason to find a second derivative is to find acceleration from a position function; the first derivative of position is velocity and the second derivative of position is acceleration.

What is a concave graph?

Concave graph is produced when a function’s slope keeps increasing or decreasing with increasing value of ‘x’. Graph thus produced would be either concave up aka ‘convex’ or concave down aka ‘concave’.

What is concave down?

Concave Down. A graph or part of a graph which looks like an upside-down bowl or part of an upside-down bowl.