Mean Value Theorem: c for f(x)=sinx on [1,1.5]

Thread starter karisrou
Start date Apr 7, 2009
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Mean Mean value theorem Theorem Value

In summary, the Mean Value Theorem is a fundamental theorem in calculus that states that for a continuous and differentiable function on a closed interval, there exists a point within that interval where the instantaneous rate of change (the derivative) is equal to the average rate of change over that interval. It is used to prove other important theorems in calculus and has practical applications in fields such as physics and engineering. The c value in the theorem refers to the point of tangency or critical point within the interval. For the function f(x) = sinx on the interval [1, 1.5], the theorem states that there exists a point c = 1.2198 where the instantaneous rate of change is equal to the average rate

Apr 7, 2009

karisrou

6. The number c satisfying the Mean Value Theorem for f(x) = sinx on the interval [1,1.5]:

So if the MVT is f(b) - f(a) / b-a

.997 - .841 / 1.5 - 1

so .156 / .5

so .312

But that isn't the correct answer. Any thoughts?

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Apr 7, 2009

n!kofeyn

Please see my post on your previous thread.

FAQ: Mean Value Theorem: c for f(x)=sinx on [1,1.5]

1. What is the Mean Value Theorem?

The Mean Value Theorem is a fundamental theorem in calculus that states that for a continuous and differentiable function on a closed interval, there exists a point within that interval where the instantaneous rate of change (the derivative) is equal to the average rate of change over that interval.

2. How is the Mean Value Theorem used?

The Mean Value Theorem is used to prove other important theorems in calculus, such as the Fundamental Theorem of Calculus. It is also used to find the points where the instantaneous rate of change is equal to the average rate of change, which has practical applications in fields such as physics and engineering.

3. What is the c value in the Mean Value Theorem?

The c value in the Mean Value Theorem is the point within the closed interval where the instantaneous rate of change (the derivative) is equal to the average rate of change over that interval. It is also known as the critical point or the point of tangency.

4. How is the Mean Value Theorem applied to the function f(x) = sinx on the interval [1, 1.5]?

For the function f(x) = sinx on the interval [1, 1.5], the Mean Value Theorem states that there exists a point c between 1 and 1.5 where the instantaneous rate of change (the derivative) is equal to the average rate of change over that interval. This point c can be found by setting the derivative of sinx equal to the average rate of change, which is (sin1.5 - sin1) / (1.5 - 1) = 0.2108. Solving for c, we get c = 1.2198.

5. What is the significance of the Mean Value Theorem for f(x) = sinx on [1, 1.5]?

The Mean Value Theorem for f(x) = sinx on [1, 1.5] tells us that there exists a point c between 1 and 1.5 where the instantaneous rate of change of the function is equal to its average rate of change over that interval. This allows us to make important conclusions about the behavior of the function, such as the existence of a tangent line at that point and the relationship between the derivative and the function itself. It also has practical applications in fields such as optimization and curve fitting.