Applications Galore (Derivatives)

If f is continuous on [a,b], then f attains an absolute min. value f(c) some number c in [a,b]

There exists a function f such that f(-1) = -2, f(3) = 0 and f'(x) > 1 for all x.

If f and g are increasing on an interval I, then f + g is also increasing on I.

There exists a function f such that f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

If f has an absolute minimum value at c, then f'(c)=0

If f and g are increasing on an interval I, then f - g is also increasing on I.

If f'(c)=0, then f has a local maximum or minimum at c.

If f and g are increasing on an interval I, then fg is also increasing on I.

If f is differentiable and f(-1) = f(1) then there is c with |c| < 1 and f'(c) = 0

If f''(2 ) = 0, then (2,f(2)) is an inflection point of the curve y = f(x).

If f'(x) = g'(x) for 0 <x < 1, then f(x) = g(x) for 0 < x < 1

If f is continuous on (a,b), then f attains an absolute min. value f(c) some number c in (a,b)

The most general antiderivative of x^-2 is -1/x +C

The most general antiderivative of xⁿ is xⁿ⁺¹/(n+1) + C for all n