Question

Consider a continuous function f that is differentiable everywhere except at x = 4 and which satisfies the following:






f ′(x) = 0 only for x = 0, 2 and 7,


lim f ′(x) = ∞,
x → 4−

lim f ′(x) = −∞,
x → 4+







f ′(−1) = 7,

f ′(1) = −4,

f ′(3) = 1,



f ′(5) = −3,

f ′(12) = −4,


f(−1) = −4,

f(1) = 1,

f(3) = 7,

f(4) = 11,

f(5) = 1,

f(12) = −4.





At which values of x does the function have a local maximum? Give your answer as a set {in curly braces}.

Answer 1

your choices are where f'(x) = 0, namely at x=0, 2 or 7

I would look at the slopes that "bracket" each "critical point"
if on the left side of the critical point the slope is rising (i.e. positive) and on the right side is decreasing (i.e. negative slope), then in between was a local max

Answer 2

phi is it possible to show diagram still don't get you