## What do derivative graphs tell you?

Simply put, an increasing function is one that is rising as we move from left to right along the graph, and a decreasing function is one that falls as the value of the input increases. If the function has a derivative, the sign of the derivative tells us whether the function is increasing or decreasing.

## What is the relationship between the graph of a function and the graph of its derivative?

Graphing the derivative with the function can illustrate how to find these turning points. The function is increasing exactly where the derivative is positive, and decreasing exactly where the derivative is negative. On the graph of the derivative find the x-value of the zero to the left of the origin.

The function f ´( x ), which would be read “ f -prime of x ”, means the derivative of f ( x ) with respect to x . If we say y = f ( x ), then y ´ (read “ y -prime”) = f ´( x ). This is even sometimes taken as far as to write things such as, for y = x 4 + 3x (for example), y ´ = ( x 4 + 3 x )´.

What is the relationship between the graph of a function in the graph of its derivative?

Finding Turning Points from the Derivative A turning point of the graph of a function is a point where the function changes from increasing to decreasing or changes from decreasing to increasing. turning point of a function has a derivative of zero at that point if it is differentiable at that point.

### How do you interpret the second derivative?

1. The Meaning of the Second Derivative.
2. The second derivative of a function is the derivative of the derivative of that function.
3. dx2 .
4. tells us if the first derivative is increasing or decreasing.
5. dx2 (p) > 0 at x = p, then f(x) is concave up at x = p.
6. • if d2f.
7. dx2 (p) < 0 at x = p, then f(x) is concave down at x = p.

### What does the first derivative tell you about the original function?

The first derivative primarily tells us about the direction the function is going. That is, it tells us if the function is increasing or decreasing. The first derivative can be interpreted as an instantaneous rate of change. The first derivative can also be interpreted as the slope of the tangent line.

How do you match a function?

The MATCH function searches for a specified item in a range of cells, and then returns the relative position of that item in the range. For example, if the range A1:A3 contains the values 5, 25, and 38, then the formula =MATCH(25,A1:A3,0) returns the number 2, because 25 is the second item in the range.