# For what values of x is #f(x)=(7x-1)(x-6)(x-2)# concave or convex?

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To determine the concavity or convexity of the function ( f(x) = (7x - 1)(x - 6)(x - 2) ), you need to find the intervals where its second derivative is positive (convex) or negative (concave).

First, find the second derivative of ( f(x) ), denoted as ( f''(x) ). Then, identify the critical points by solving for ( f''(x) = 0 ) and analyze the sign of ( f''(x) ) in the intervals between these critical points.

To summarize:

- Find ( f''(x) ).
- Determine critical points by solving ( f''(x) = 0 ).
- Analyze the sign of ( f''(x) ) in each interval defined by the critical points.

Once you determine the intervals where ( f(x) ) is concave or convex, you can state the values of ( x ) within those intervals.

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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.

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