Answer true or false. If f, g, and h are differentiable functions, and h $\neq$ 0 anywhere on its domain, then .

Question

Answer true or false. If f, g, and h are differentiable functions, and h $\neq$ 0 anywhere on its domain, then  .

Quizplus · Accepted Answer

This statement is a direct application of the quotient rule of differentiation, which states that if f and g are differentiable functions and g is nonzero anywhere on its domain, then (f/g)' = (f'g - fg')/g^2. In this case, letting F = f/g, we have F' = (f'g - fg')/g^2, and since h is also differentiable and nonzero, we can differentiate again to obtain F'' = [f''g + 2f'g' - g''f]/g^3, which is also well-defined and nonzero. Thus, F has a nonzero second derivative, which implies that it is not constant.

Answer True or False ≠\neq= 0 Anywhere on Its Domain, Then

Answer True or False $\neq$ 0 Anywhere on Its Domain, Then