stationary point

1. DETERMINING THE COEFFICIENT OF ARAN tangents

    (Gradient) at the point (x1y1) on the curve y = f (x)

   

m = f '(x1)

f '(x1) means the value of the derivative f (x) at the point with abscissa x = x1,

Note:

Especially for a quadratic function. If the point does not lie on the graph, the gradient of the tangent is exemplified by m that found using the line equation y - y1 = m (x - x1) disinggungkan curve with equation y = f (x) with the condition D = 0 (D = discriminant of elimination results two equations)

2. DETERMINING THE FUNCTION monotonous

• The function y = f (x) monotonically rising at an interval,

                         if the interval is valid f '(x)> 0

• The function y = f (x) monotonically down on an interval,

                         if the interval is valid f '(x) <0

3. DETERMINING THE STATIONARY POINT

Function y = f (x) ® Terms stationary f '(x) = 0

TYPE - KIND

STATIONARY:

MAXIMUM

Terms: f '(x) = 0 ® x = x0 f'' (x0) <0 ® The maximum point (xo, f (xo))

MINIMUM

Terms: f '(x) = 0 ® x = x0 f'' (x0)> 0 ® Minimum point (xo, f (xo))

TURNING

Terms: f '(x) = 0 ® x = x0 f'' (x0) = 0 ® inflection point (xo, f (xo))

Stationary value is the value of a function at a stationary point abscissa

Description:

1. To determine the types of stationary point can also be searched by looking at the change marks around a stationary point.

   Steps:

   a. Determine abscissa stationary point condition f '(x) = 0 ® x = xo

   b. Create a number line f '(x)

   c. Determine the signs around the stationary point by substituting an arbitrary point on f '(x)

   d. Type the stationary point is determined by the change in sign around

       stationary point.

ket: f '(x)> 0 the graph up

       f '(x)> 0 the graph down

2. The maximum value / minimum of a function in a closed interval obtained from the stationary value or function in the interval of the value of the function at the end - the end of the interval

4. PHYSICS PROBLEM

If S (t) = distance (a function of time)

      V (t) = Speed ​​(function of time)

      a (t) = Acceleration (function of time)

          t = time

then V = dS / dt and a = dV / dt

5. TROUBLESHOOTING LIMIT

L'Hospital theorem

If the functions f and g respectively terdifferensir at x = a and f (a) = g (a) = 0 or f (a) = g (a) = ¥ thus:

 lim f (x) = 0 or lim f (x) = ¥, then

x ® a g (x) 0 x ® a g (x) ¥

 lim f (x) = lim f '(x) = ¥, then

x ® a g (x) x ® a g '(x) ¥