Consider the function
Find the equation of the tangent line to
to find the slope, and evaluate to find the -intercept. Use the point-slope formula to create the equation of the tangent line.
using part (a).
Use the tangent line at
to evaluate . This will approximate . Why approximate?
Since a tangent is a linear equation, it is easier to evaluate than
to justify whether part (b) is an under or over approximation of the actual value.
A concave up graph has tangent lines that are below the curve. Sketch it, you will see.
And a concave down graph has tangent lines that are above the curve.