Consider the curve
Find the equation of the tangent line at
Notice that the derivative you found in part (a) has both
- and -values.
, estimate using the tangent line.
is easier to evaluate in a linear equation than in the curve shown above, use the tangent line to estimate the -value at .
, determine if the tangent approximation is an over or under estimate. Justify your answer in words.
, remember to substitute your answer in part (a).
The sign of the 2nd derivative at
will determine if the tangent line is above or below the curve.
When a function is concave up, the tangent line will be below the curve.
When it is concave down, the tangent line will be above the curve.
Verify these statements by sketching a few examples.