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Numerade Educator

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Problem 43 Hard Difficulty

Suppose that the only information we have about a function $ f $ is that $ f(1) = 5 $ and the graph of its $ derivative $ is as shown.
(a) Use a linear approximation to estimate $ f(0.9) $ and $ f(1.1). $
(b) Are your estimates in part (a) too large or too small? Explain.

Answer

(a) $4.8,5.2$
(b) Too Large

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Video Transcript

Okay, First things first. We know we have after 0.9 is off of one minus zero point one, which is half of one class after prime of one times negative 0.1, which is five minus two time 0.1, which is 4.8. So now we have half of 1.1 is half of one plus off. Prime of one come 0.1 is five plus chu time 0.1, which is 5.2. Okay, So part B, as we can see after prime of access positive and decreasing there for the slopes of the tangent lines are positive and are becoming less steep. Therefore, we know that because the tangent line is above the curve of f of axe, we know the estimates must be too big. So it's an overestimate above the curve.