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.
Fikiria kazi Kupata equation ya mstari tangent kwa kupata mteremko, na kutathmini kupata -intersection. Tumia pointi-mteremko formula kuunda equation ya mstari tangent. kutumia sehemu (a). Tumia tangent line katika kutathmini. Hii itakuwa takriban. Kwa nini ni takriban? Tangu tangent ni linear equation, ni rahisi kutathmini kuliko kuthibitisha kama sehemu (b) ni chini au juu ya makadirio ya thamani halisi. Concave juu grafu ina tangent mistari ambayo ni chini ya curve. Boresha, utaona. Grafu ya concave-down ina tangent line juu ya curve.