## What is the derivative of a graph?

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value.

**What does the second derivative graph tell you?**

The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph is concave down.

### What does the derivative of a function look like on a graph?

The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where f(x) has a tangent line with positive slope, f′(x)>0.

**How do you graph a derivative on Desmos?**

To enter the prime symbol, you can click on the ‘ button located on standard keyboards. f′(x) can be used to graph the first order derivative of f(x) . Use f′′(x) to find the second derivative and so on. If the derivative evaluates to a constant, the value is shown in the expression list instead of on the graph.

#### What does it mean if the second derivative is less than 0?

2. The second derivative is negative (f (x) < 0): When the second derivative is negative, the function f(x) is concave down. 3. The second derivative is zero (f (x) = 0): When the second derivative is zero, it corresponds to a possible inflection point.

**What does second derivative tell you?**

Positive first derivative means an increasing function.

## How to estimate a derivative from a graph?

– If changes sign from positive when to negative when then is a local maximum of – If changes sign from negative when to positive when then is a local minimum of – If has the same sign for and then is neither a local maximum nor a local minimum of

**What does first and second derivative mean?**

– The first one is how position is changing over time. So, at periodic points, the position is measured. – The second one is the measure of speed (because we are not considering direction), how much the position changes per unit time period. This is the first derivative. – The third one is the acceleration, how much the velocity changes per unit time period.

### What are first and second derivatives?

If f” (x) < 0,then the function f (x) has a local maximum at x.