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A more complete question is required to receive a good answer here. If you were to ask how to derive a function, I could take you through a general rundown of the basic derivative patterns of most common functions. Since you said "equation" though, this implies the possibility of implicit differentiation methods being required. If you were to narrow down your question more, you might get a better answer.
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How do you find the Min value for y in this equation?
You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
How do you find the derivitive of an equation?
An equation may or may not have a derivative. The derivative of a function f(x), is usually defined as the limit as h tends to 0, of [f(x+h) - f(x)]/h
If the 2nd derivative of an equation isn't constant is it still a quadratic relation?
No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
How do you find the maximum or minimum of a parabola?
Solve for when the first derivative is equal to zero. If you don't know how to take a derivative, then put the equation into the form y = Ax2 + Bx + C. The derivative of this will be 2Ax + B, so at x = -B / (2*A), and y = -B2/(4*A) + C
How do you find the equation of a tangent line?
In order to find the equation of a tangent line you must take the derivative of the original equation and then find the points that it passes through.
How do you find the Min value for y in this equation?
You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
How do you find the derivitive of an equation?
An equation may or may not have a derivative. The derivative of a function f(x), is usually defined as the limit as h tends to 0, of [f(x+h) - f(x)]/h
What is the significance of the slope in the graphs?
This is the first fundemental theorem of Calculus. The slope of a line is very important in your first calculus course. The slope tells you the rate of change. This means how much is the object change in height compared to its change in length. The slope of a line in Calculus is used as the first derivative. If you can take the slope of a line at one particular point you will find the answer to the derivative at this point. Remember this. You first equation on your graph is called your position equation. If you take the derivative of this equation it is called the velocity equation. The velocity equation is how much the position equation is sloping at each point. If you take the derivative of the velocity equation you will get the acceleration equation. The accerelation equation is how much the velocity is sloping at each point. You can take the derivative of the acceleration equation and this will give you the jerk equation. The jerk equation is not used in many applications and I have never used this equation in any of my 4 calculus classes.
If the 2nd derivative of an equation isn't constant is it still a quadratic relation?
No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6
What is second order differential equation?
The highest order of derivative is 2. There will be a second derivative {f''(x) or d2y/dx} in the equation.
Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
What is the calculus operation for finding the rate of change in an equation?
A derivative.
How do you find the maximum or minimum of a parabola?
Solve for when the first derivative is equal to zero. If you don't know how to take a derivative, then put the equation into the form y = Ax2 + Bx + C. The derivative of this will be 2Ax + B, so at x = -B / (2*A), and y = -B2/(4*A) + C
What is the derivative of x-y?
The partial derivative in relation to x: dz/dx=-y The partial derivative in relation to y: dz/dy= x If its a equation where a constant 'c' is set equal to the equation c = x - y, the derivative is 0 = 1 - dy/dx, so dy/dx = 1
Slope of an equation?
For a straight line (a linear equation), solve the equation for "y". That will give you an equation of the form: y = mx + b In this case, "m" is the slope (and "b" is the y-intercept). For an arbitrary equation, solve it for "y" again. Then you need to take the derivative. There are various rules for taking the derivative; you can see an overview in the Wikipedia article on "Derivative", but to understand the concept better, you should read an introductory calculus book.
