Ch.3 Differentiation

Question 1

Limit definition of derivative

Answer 1

f’(a) = lim (f(a+h) - f(a)) / h

(h–>0)

Question 2

The second derivative test

Answer 2

If f’‘(a) > 0 then x=a is a local minimum

If f’‘(a)

Question 3

State Rolle’s theorem

Answer 3

If f is differentiable on the open interval (a,b) and continuous on the closed interval [a,b], with f(a) = f(b), then there is at least one c in (a,b) s.t f’(c) = 0

Question 4

State the mean value theorem

Answer 4

If f is differentiable on the open interval (a,b) and continuous on the closed interval [a,b], then there is at least one c in (a,b) s.t
f’(c) = (f(b) - f(a)) / (b-a)

Question 5

State the inverse function rule

Answer 5

If f(x) is continuous on [a,b] and differentiable on (a,b) with f’(x) > 0 throughout this interval then its inverse function g(y) is differentiable for all f(a)

Question 6

Partial derivative of f with respect to x

Answer 6

Differentiate f with respect to x, keeping y fixed