   Chapter 2.5, Problem 45E

Chapter
Section
Textbook Problem

For what value of the constant c is the function f continuous on ( –∞, ∞)? f ( x ) = { c x 2 + 2 x   if   x < 2 x 3 − c x       if   x ≥ 2

To determine

To find: The value of c which satisfies the function f(x) to be continuous on the interval (,).

Explanation

Given:

The function is f(x)={cx2+2xifx<2x3cxifx2, where c is the constant.

Theorem used:

The functions such as “Polynomials, rational functions, root functions, trigonometric functions, inverse trigonometric functions, exponential functions and logarithmic functions” are continuous at every number in their domains.

Calculation:

Consider the function f(x)={cx2+2xifx<2x3cxifx2.

Here, the given function is polynomial piecewise function and also polynomial is always continuous. Therefore, cx2+2x is continuous on (,2) and x3cx is continuous on (2,)

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