By applying the definition of continuity and knowing piecewise functions, we know that the solution to this system of linear equations is c = 10 and d = -8.
How to make a piecewise function continuous
According to the functional theory, functions are continuous for a given interval if and only if the function has an only value for each element of the interval. In the case of the piecewise function, we must observe these two conditions:
2 · x = c · x² + d, for x = 1 (1)
4 · x³ = c · x² + d, for x = 2 (2)
Then, we have the following system of linear equations:
c + d = 2 (1b)
4 · c + d = 32 (2b)
The solution to this system of linear equations is c = 10 and d = -8.
To learn more on piecewise functions: https://brainly.com/question/12561612
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