Question

Let f(x) be a polynomial function such that f(-5)=1, f'(-5)=0, and f''(-5)= -2. the point (-5,1) is a ________ of the graph of f. what is the Blank?

Answer 1

local/relative maximum

Explanation:

`f(-5)` doesnt matter for this problem
`f'(-5)=0` means tangent line at `x=-5` is horizontal
since `f''(-5)` is negative, the graph is concave down, so `(-5,1)` is a local/relative maximum

check this video

this is a possible graph (`f(x)=-(x+5)^2+1`) (not necessarily the actual equation) graph{-(x+5)^2+1 [-10, 10, -5, 5]}