Consider the curve xe5y = 3y. Homework Help ✎
Find the equation of the tangent line at (0, 0).
If x = 0.1, estimate y using the tangent line.
, determine if the tangent approximation is an over or under estimate. Justify your answer in words.
Notice that the derivative you found in part (a) has both x- and y-values.
Since x = 0.1 is easier to evaluate in a linear equation than in the curve shown above, use the tangent line to estimate the y-value at x = 0.1.
The sign of the 2nd derivative at (0,0) will determineif 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.