Posted by **Elizabeth** on Monday, October 15, 2012 at 9:57pm.

suppose f(x) is a function such that f(3)=5, f'(3)=0, and f''(3)=3. Is the point (3, 5) a relative maximum, minimum or inflection point?

- calculus -
**Reiny**, Monday, October 15, 2012 at 11:04pm
f ' (3) = 0 tells me that at the point (3,5) the tangent is horizontal, so (3,5) must be either a maximum or a minimum.

f '' (3) = 3 tell sme that at the point (3,5) the curve is concave up, so

(3,5) must be a minimum point.

(it couldn't possibly be a point of inflection or else the f '' (3) would have been 0 )

## Answer this Question

## Related Questions

- Calculus - Let f(x) be a polynomial function such that f(-2)=5, f’(-2)=0 and f...
- Calculus - Let f(x) be a polynomial function such that f(-2)=5, f'(-2)=0, and f...
- Calculus check - Let f(x) be a polynomial function such that f(3)=3, f'(3)=0 and...
- Calculus - Let f(x) be a polynomial function such that f(4)=-1, f’(4)=2 and f”(4...
- math - Suppose p(x) is a twice-differentiable function such that p(1) = 3, p'(1...
- Calculus AB - Find a, b, c, and d such that the cubic function ax^3 + bx^2 + cx...
- calculus - I needed help with these FRQ in my APCalc course. Any help or ...
- Pre-calculus - Find the critical point of the function y=-2(x-1)^2-3. Then, ...
- Pre-calculus - Find the critical point of the function y=-2(x-1)^2-3. Then, ...
- Calculus - Which statement is NOT true of the graph f(x)=(x+1)(x-3)^2? A. f has ...

More Related Questions