Question

let f(x) be a polynomial function such that f(3)= 3 f'(3)=0 and f"(3)=-3 what is the point (3,3) on the graph y= f(x)?

Answer 1

it is a local maximum

Answer 2

slope of tangent is zero, function is concave down

Answer 3

Did you just look at it and know or is there something you did? Because It just doesn't come to me right away -__-

Answer 4

i know in my head that if the derivative is zero, then you MAY have a local max or min (it may be neither) but that if the second derivative is negative then the function is concave down, so it must be a local max. that is why i inserted the picture, to show what i was thinking in my head from the information given

Answer 5

clearly there is nothing to compute, because you do not even know what the function is. so you have to use the information as you see it

Answer 6

aahhh ok thank you, I'll keep this in mind next time :)