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Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than the value at the first point.

Front

How do you determine the interval where a function is increasing or decreasing?

Back

To determine the intervals where a function is increasing or decreasing, analyze the function's derivative. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What is the formula to isolate variable c in the equation a = b + c?

Back

c = a - b.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation and simplify.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

Front

Given the sequence 17, 12, 7, 2, what is the common difference?

Back

The common difference is -5.

Front

What is a mistake in a mathematical step?

Back

A mistake in a mathematical step is an error in calculation or reasoning that leads to an incorrect conclusion.

Front

How can you identify mistakes in a sequence of mathematical steps?

Back

To identify mistakes, review each step for accuracy in calculations and logical consistency.

Front

What is the significance of the derivative in understanding function behavior?

Back

The derivative indicates the rate of change of a function, helping to determine where it is increasing, decreasing, or constant.

Front

What does it mean if a function has no mistakes in its steps?

Back

It means that all calculations and logical deductions are correct, leading to a valid conclusion.