Consider the function
Write the equation of the line tangent to
to find the slope, and evaluate to find the y-intercept. Use the point-slope formula to create the equation of the tangent line.
using your answer to 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
Is your approximation an underestimate or an overestimate of the actual value? Explain.
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.