a), yes true,
setting f''(x) = 0 gives you the point of inflection,
which is where the concavity changes
b) not true,
counterexample:
let f(x) = 2x^2 - 12x + 22
in the interval [1,8] the graph is entirely above the x-axis, and f'(x) = 4x - 12
f '(3) = 0
so I found a value of x for which the derivative is zero in the given interval but there is no root in the given interval
We have to find out which of these statements are true. I narrowed it down to 2 answers.
a) if f"(0)=0, the the graph of f changes concavity at x=0
b) If the function f is continuous on the interval [a,b] and the integral from a to b of f(x)dx=0, then f must have at least on zero between a and b
2 answers
THANK YOU SO MUCH!
1 answer