The temperature (in degrees Celsius) of an engine during a test run is modeled for…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The temperature (in degrees Celsius) of an engine during a test run is modeled for 0≤t≤10 minutes by the function
h(t)=100+20ln(t+1).
A technician records exact data at t=4 minutes but needs an immediate estimate at t=4.3 minutes.
(1) Find the equation of the tangent line to the graph of y=h(t) at t=4. Write your answer in slope–intercept form.
(2) Using the tangent line from part (a), estimate the engine temperature at t=4.3 minutes. Round your answer to the nearest tenth of a degree Celsius.
(3) Decide whether the estimate found in part (b) is higher or lower than the actual temperature at t=4.3 minutes. Support your decision with a convincing argument based on characteristics of h on an interval containing t=4. No numerical evaluation of h(4.3) is required.