Ray 4 said:Homework Statement
find the difference quotient and simply your answer.
f(t)=1/t, [f(t)-f(1)]/t-1, t doesn't equal 1
Homework Equations
the book says the answer is -1/t, t doesn't equal 1
The Attempt at a Solution
(1/t-1)/t-1
(1/t-t/t)/t-1
(-1t/t)/t-1
-1/t-1
thanks!
danago said:How did you get that line?
The formula for finding the difference quotient is (f(x+h) - f(x)) / h, where h is the change in the x-value and f(x) is the original function.
To simplify the difference quotient, you can start by expanding the numerator and simplifying any like terms. Then, you can factor out the h in the denominator and cancel out any common factors between the numerator and denominator.
Yes, the difference quotient can be used to find the slope of a curve at a specific point on the curve. However, as h approaches 0, the difference quotient becomes the derivative of the function.
Finding the difference quotient allows us to approximate the slope of a curve at a specific point. This can be useful in many applications, such as calculating instantaneous velocity or acceleration in physics.
One limitation of using the difference quotient is that it only gives us an approximation of the slope at a specific point. To find the exact slope, we would need to take the limit as h approaches 0, which can be computationally challenging for more complex functions.