sulagna_palit
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BC Calc Question
- Thread starter sulagna_palit
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Please show us what you have tried and exactly where you are stuck.
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HallsofIvy
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The very first problem asks you to find the average rate of change of f(x) between two points.
I strongly suspect that in the same chapter where you are given the problem, the book defines "average rate of change" of f(x) between x= a and x= b as (f(b)- f(a))/(b- a). What are a, b, f(a), and f(b) here?
I don't know how your text handles it but many Calculus texts define the derivative of f at x= a as "the slope of the tangent line to y= f(x) at the point (a, f(a))." So the tangent line to y= f(x) at x= -3 is y= f'(-3)(x- (-3))= f'(-3)(x+ 3). What is f'(-3)?
The average value of f between a and b (as opposed to the average rate of change of f) is \(\displaystyle \frac{\int_a^b f(x)dx}{b- a}\). What is \(\displaystyle \int_{-3}^4 f(x)dx\)?
Every continuous function attains both maximum and minimum values on a closed bounded interval. Is this a closed and bounded interval? Is f continuous?
I strongly suspect that in the same chapter where you are given the problem, the book defines "average rate of change" of f(x) between x= a and x= b as (f(b)- f(a))/(b- a). What are a, b, f(a), and f(b) here?
I don't know how your text handles it but many Calculus texts define the derivative of f at x= a as "the slope of the tangent line to y= f(x) at the point (a, f(a))." So the tangent line to y= f(x) at x= -3 is y= f'(-3)(x- (-3))= f'(-3)(x+ 3). What is f'(-3)?
The average value of f between a and b (as opposed to the average rate of change of f) is \(\displaystyle \frac{\int_a^b f(x)dx}{b- a}\). What is \(\displaystyle \int_{-3}^4 f(x)dx\)?
Every continuous function attains both maximum and minimum values on a closed bounded interval. Is this a closed and bounded interval? Is f continuous?