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?

Question

Mathematics

Gunnar Medina

10 April, 02:40

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?

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Answers (1)

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Luis Beasley · Answer 1

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