Question

Find the derivative of the function using the definition of derivative. G(t) = 1 − 2t 5 + t G'(t) = Incorrect: Your answer is incorrect. State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)

Answer 1

Answer:

a) G'(t) = -11/(5+t)²

b) Domain of the function

(-∞ < t < -5) and (-5 < t < ∞)

c) Domain of the derivative too

(-∞ < t < -5) and (-5 < t < ∞)

Step-by-step explanation:

a) Obtaining the derivative of the function from the definition of a derivative is presented in the attached image to the question.

b) Domain of the function includes every value of t for which the function exists.

The function only ceases to exist when the function goes to ±∞.

And this occurs when the denominator = 0

The function does not exist at (5 + t) = 0; t = -5.

So, the function exists in every domain of real numbers except at t = - 5

Hence, the domain of the function is (-∞ < t < -5) and (-5 < t < ∞)

c) Domain of the derivative

This is similar to the domain of the function.

The derivative ceases to exist only when

(5+t)² = 0; t = - 5

Hence, the domain of the derivative too is (-∞ < t < -5) and (-5 < t < ∞)