Question 1140452
<pre>
The first obvious thing to do is use the identity 

{{{sin(theta-pi/2)=-cos(theta)}}} to simplify.

{{{y = 4sin(expr(pi/4)(x) - pi/2) - 3}}} becomes

{{{y = -4sin(expr(pi/4)(x)) - 3}}}

Its average (not instantaneous!) rate of change over {{{P<=x<=Q}}}

is  

{{{Delta(y)= (-4sin(expr(pi/4)(Q))^"" - 3^"")-(-4sin(expr(pi/4)(P))^"" - 3^"")}}}

which simplifies to

{{{Delta(y)= 4(sin(expr(pi/4)(P))-sin(expr(pi/4)(Q))^"")}}}

Then we use the identity: {{{sin(alpha)-sin(beta)=2sin((alpha-beta)/2)cos((alpha+beta)/2)}}}

I won't go through the details, but that simplifies to

{{{8(sin((A*pi)/8 - (B*pi)/8)cos((A*pi)/8 + (B*pi)/8)^"")}}}}
Now you finish by solving this equality:

{{{8(sin((A*pi)/8 - (B*pi)/8)cos((A*pi)/8 + (B*pi)/8)^"")=0}}}

to find some zeros which will be answers to c) and which
will also be critical numbers for a) and b).  Then solve this

{{{8(sin((A*pi)/8 - (B*pi)/8)cos((A*pi)/8 + (B*pi)/8)^"")>0}}}

for a)

and this

{{{8(sin((A*pi)/8 - (B*pi)/8)cos((A*pi)/8 + (B*pi)/8)^"")<0}}}

for (b)

Edwin</pre>