if it is known, for a continuous differentiable function f(x), f'(c)=0 and f''(c)=0, what can be concluded about the graph of f(x) at x=c ?
1. The tangent to the curve is horizontal 2. There must be a point of inflection 3. The curve must be a straight line because the curvature is 0 4. There is an extremum and a point of inflection and the same place 5. The curve must be a straight line if the derivatives are 0
There may be more than 1 correct answer.
I am having a hard time thinking any of them are true. I know that 5 would make sense but not if the equation is x^4 since the derivative of that at 0 would be 0. When it says the tangent to the curve is horizontal is it talking about just at that point of c? Thank you for the help!