Ch. 8 Differentiable Functions

Question 1

Definition of a function f being differentiable at c

Answer 1

f is differentiable at c if:
lim(x–>c) (f(x) - f(c)) / (x - c) exists

It is differentiable if it is differentiable at all points

Question 2

State The Mean Value Theorem

Answer 2

Let f:[a,b] be continuous and differentiable on (a,b) then there exists a c in (a,b) s.t
f’(c) = (f(b) - f(a)) / (b-a)

Question 3

State Rolle’s Theorem

Answer 3

if f is continuous on [a,b], and f(a) = f(b), then there exists at least 1 c in (a,b) such that f’(c) = 0