Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
Step-by-step explanation:
Used:
Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function is shown in the graph attached herein. (Correct choice: A)
<h3>How to determine a piecewise function</h3>
In this question we have a graph formed by two different <em>linear</em> functions. <em>Linear</em> functions are polynomials with grade 1 and which are described by the following formula:
y = m · x + b (1)
Where:
- x - Independent variable.
- y - Dependent variable.
- m - Slope
- b - Intercept
By direct observation and by applying (1) we have the following <em>piecewise</em> function:
Based on the characteristics of <em>linear</em> and <em>piecewise</em> functions, the <em>piecewise</em> function is shown in the graph attached herein. (Correct choice: A)
To learn more on piecewise functions: brainly.com/question/12561612
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Answer:
(x +yi)²
Step-by-step explanation:
Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.
(a +b)² = a² +2ab +b²
Here, we have a=x and b=yi. Then the factorization is ...
x² +2xyi +(yi)² = (x +yi)²
Original price:
6(3.5)
21
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1.15(21)
24.15
24.15-21
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