Casio FX-CG10 Software User Guide - Page 75
Second Derivative Calculations, Using Second Derivative Calculation in a Graph Function
View all Casio FX-CG10 manuals
Add to My Manuals
Save this manual to your list of manuals |
Page 75 highlights
k Second Derivative Calculations [OPTN]-[CALC]-[d2/dx2] After displaying the function analysis menu, you can input second derivatives using the following syntax. K4(CALC)3(d2/dx2) f(x)ea or 4(MATH)5(d2/dx2) f(x)ea K4(CALC)3(d2/dx2) f(x),a) a is the point for which you want to determine the second derivative. -dd-x2-2 ( f (x), a) ⇒ -dd-x-22 f (a) Second derivative calculations produce an approximate derivative value using the following second derivative formula, which is based on Newton's polynomial interpretation. 2 f(a + 3h) - 27 f(a + 2h) + 270 f(a + h) - 490 f(a) + 270 f(a - h) - 27 f(a -2h) + 2 f(a - 3h) f ''(a) = 180h2 In this expression, values for "sufficiently small increments of h" are used to obtain a value that approximates f"(a). Example To determine the second derivative at x = 3 for the function y = x3 + 4x2 + x - 6 Input the function f(x). AK4(CALC)3(d2/dx2)vMde+evx+v-ge Input 3 as point a, which is the derivative point. dw Using Second Derivative Calculation in a Graph Function You can omit input of the value a in the syntax above by using the following format for the second derivative graph: Y2 = d2/dx2 (Y1). In this case, the value of the X variable is used instead of the value a. Second Derivative Calculation Precautions The precautions that apply for first derivative also apply when using a second derivative calculation (see page 2-28). 2-29