## What is the derivative of a parametric curve?

The derivative of the parametrically defined curve x=x(t) and y=y(t) can be calculated using the formula dydx=y′(t)x′(t). Using the derivative, we can find the equation of a tangent line to a parametric curve.

### What is the difference between implicit and parametric differentiation?

my understanding is that implicit differentiation sets a variable as a function of another, whereas in parametric equations, we set 2 variables as the function of another.

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

The second derivative measures the instantaneous rate of change of the first derivative. The sign of the second derivative tells us whether the slope of the tangent line to f is increasing or decreasing.

**Is implicit derivative and implicit differentiation the same?**

Implicit differentiation is the process of differentiating an implicit function which is of the form f(x, y) = 0 and finding dy/dx. To find the implicit derivative, Differentiate both sides of f(x, y) = 0 with respect to x. Apply usual derivative formulas to differentiate the x terms.

## What is d2y dx2 used for?

The second derivative is written d2y/dx2, pronounced “dee two y by d x squared”. The second derivative can be used as an easier way of determining the nature of stationary points (whether they are maximum points, minimum points or points of inflection).

### What does the second derivative mean on a graph?

The second derivative is acceleration or how fast velocity changes. 🔗 Graphically, the first derivative gives the slope of the graph at a point. The second derivative tells whether the curve is concave up or concave down at that point.

**What does the second derivative tell you about concavity?**

The Second Derivative Test relates to the First Derivative Test in the following way. If f″(c)>0, then the graph is concave up at a critical point c and f′ itself is growing. Since f′(c)=0 and f′ is growing at c, then it must go from negative to positive at c.

**How do you eliminate the parameter of a parametric equation?**

- One of the easiest ways to eliminate the parameter is to simply solve one of the equations for the parameter (t t , in this case) and substitute that into the other equation.
- In this case we can easily solve y y for t t .
- Plugging this into the equation for x x gives the following algebraic equation,

## How do you turn a parametric equation into a function?

The process for converting parametric equations to a rectangular equation is commonly called eliminating the parameter. First, you must solve for the parameter in one equation. Then, substitute the rectangular expression for the parameter in the other equation, and simplify.