Question

Find the maximum value of 5 + $(sinx-4{)}^2$

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Answer 1

Maximum value of 5 + $(sinx-4{)}^2$ is 5 + maximum value of $(sinx-4{)}^2$. So we want to find the maximum value of $(sinx-4{)}^2$

Sinx varies from -1 to 1.|sinx - 4| is the distance of sinx from 4.This distance is maximum when sinx is -1 $(sinx-4{)}^2$ will be maximum when |sinx - 4| is maximum.This happens when sinx = -1

$\Rightarrow$ Maximum value = 5 + $(-1-4{)}^2$

= 5 + $5^2$

= 30