When is $I(c) = \int^1_0 2^{-(x-c)^2} dx$ largest?
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Ref: R7461

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Let $c$ be a real number and define the following integral \[I(c) = \int^1_0 2^{-(x-c)^2} dx.\]

State the value(s) of $c$ for which $I(c)$ is largest. Briefly explain your reasoning. [Note you are not being asked to calculate this maximum value.]

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The curve here is $y = 2^{-(x-c)^2}$, and the white region is $I(c)$.

Before moving the slider, what effect will it have on the curve?

When will $I(c)$ have its largest value?

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Calculus meets Functions

When is $I(c) = \int^1_0 2^{-(x-c)^2} dx$ largest? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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When is $I(c) = \int^1_0 2^{-(x-c)^2} dx$ largest?
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