Review question

# 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

Ref: R7461

## Question

1. The graph $y = f(x)$ of a certain function has been plotted below.

On the next three pairs of axes (A), (B), (C) are graphs of $y = f(-x), \quad f(x-1), \quad -f(x)$ in some order. Say which axes correspond to which graphs.

2. Sketch graphs of both of the following functions $y = 2^{-x^2} \quad \text{and} \quad y = 2^{2x - x^2}.$ Carefully label any stationary points.

3. 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.]