Question

Find the derivative of the function using the definition of derivative. g(t) = 7 t g'(t) = 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:

$R = \{ \forall x \in \mathbf{R}|-\infty < x < \infty\}$

Step-by-step explanation:

The definition of derivative states that:

$g'(t) = \lim_{h \to 0} \frac{g(t+h)-g(t)}{h}$

Then:

$g'(t) = \lim_{n \to \infty} \frac{7\cdot (t+h)-7\cdot t}{h}$

$g'(t) = \lim_{h \to 0} 7$

$g'(t) = 7$

A constant function is a zero-order polynomial. The domain of any real polynomial is $\mathbf{R}$. Then, the domain of the function is:

$R = \{ \forall x \in \mathbf{R}|-\infty < x < \infty\}$