L1 (x) for x<0, f=\"\" x=\"\" for=\"\" 0=\"\" 100=\"\" and=\"\" l2=\"\"> 100] do
ID: 3186539 • Letter: L
Question
L1 (x) for x<0, f="" x="" for="" 0="" 100="" and="" l2=""> 100] doesn't have a continuous second derivative. So decide to improve the design by using a quadratic function q(x)=ax^2+bx+c only on the interval 10 less than or equal x less than or equal to 90 and connecting it to linear functions by means of two cubic functions: g(x)= KC^3+ lx^2+mx+n 0<x<10 h(x)= PX^3+qx^2+ RX+ S 90<X100
A) Write a system of equations in 11 unknowns that ensure that the functions and their first two derivatives agree at the transition points.
B) find formulas for q(x),g(x), and h(X)
C) Plot L1,G,Q, H, and L2
Explanation / Answer
Help: At point x=0, values of L1 and g(x) are equal, as well as the derivatives and second derivatives. At point x=10, g(10) = q(10); and g'(10) = q'(10); second derivatives as well. At point x = 90, q(90) = h(90); q'(90) = h'(90) and same holds true for second derivatives. At x=100, h(100) = L2(100), and the first/second derivatives agree. In the case of both lines, the second derivative is 0, which will help you determine g and h, along with the other equations that equate these points. matrix will be as follow |k....l....m....n| |x³|.........|g(x)| |p....q....r.....s| |x²|......=.|h(x)| |a....b....c....0| |x |.........|q(x)|
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