Question

The derivative of the function B is given by B′(t)=8e0.2cost , and B(2.2)=4.5 . If the linear approximation to B(t) at t=2.2 is used to estimate B(t) , at what value of t does the linear approximation estimate that B(t)=9 ?

Answer 1

Answer:

The linear approximation of B(t) at t = 2.2 estimates B(t) = 9 for t = 2.8328

Step-by-step explanation:

b'(2.2) = 8 * e^(0.2cos(2.2)) = 7.1117 and b(2.2) = 4.5. The linear approximation of B(t) at t = 2.2 is

L(t) = 7.1117*(t-2.2) + 4.5

We want t so that L(t) = 9

9 = 7.1117*(t-2.2) + 4.5

4.5 = 7.1117 *(t-2.2)

t-2.2 = 4.5/7.1117 = 0.6327601

t = 2.2+0.6327601 = 2.8328