- #1
Unusualskill
- 35
- 1
(a) State precisely the definition of: a function f is differentiable at a ∈ R.
(b) Prove that, if f is differentiable at a, then f is continuous at a. You may
assume that
f'(a) = lim {f(x)-f(a)/(x-a)} as x approaches a
(c) Assume that a function f is differentiable at each x ∈ R and also f(x) > 0
for all x ∈ R. Use the definition of the derivative and standard limit laws to
calculate the derivative of:
g(x) = (f(x))^0.25
in terms of f(x) and f'(x).
Im stuck at part(c)...Can guide me or show me how to start?thx alot!
(b) Prove that, if f is differentiable at a, then f is continuous at a. You may
assume that
f'(a) = lim {f(x)-f(a)/(x-a)} as x approaches a
(c) Assume that a function f is differentiable at each x ∈ R and also f(x) > 0
for all x ∈ R. Use the definition of the derivative and standard limit laws to
calculate the derivative of:
g(x) = (f(x))^0.25
in terms of f(x) and f'(x).
Im stuck at part(c)...Can guide me or show me how to start?thx alot!