# For what values of x is #f(x)= -x^3+3x^2+2x-12 # concave or convex?

As viewed from O, concave

y''--6(x-1)=0#, at x =1.

Here, the tangent crosses the curve, reversing rotation, from

anticlockwise to clockwise.

graph{-x^3+3x^2+2x-12 [-29.95, 29.95, -14.97, 14.98]}

graph{(-x^3+3x^2+2x-12-y)(y+8)=0 [-2, 2, -20, 20]} .

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you determine whether the function #f(x)= (lnx)^2# is concave up or concave down and its intervals?
- How do you find points of inflection and determine the intervals of concavity given #y=1/(x-3)#?
- What are the points of inflection, if any, of #f(x)= (x^2+x)/(x^2+1) #?
- For what values of x is #f(x)= x + 1/x # concave or convex?
- How do you find all points of inflection given #y=x^2/(2x+2)#?

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