(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a function of the form [tex] f(x) = a + b \cos cx [/tex] that is tangent to the line [tex]y = 1[/tex] at the point [tex](0,1)[/tex], and tangent to the line [tex]y = x + 3/2 - \pi /4[/tex] at the point [tex](\pi /4 , 3/2)[/tex].

2. Relevant equations

3. The attempt at a solution

[tex]f(0) = a + b = 1[/tex], so [tex]a = 1 - b[/tex].

This is as far as I can get though.

[tex]f'(0) = -bc \sin cx = 0[/tex]

for any a, b, and c, and

[tex]f(\pi /4) = (1 - b) + b \cos [(\pi /4)c] = 3/2[/tex]

and

[tex]f'(\pi /4) = -bc \sin [(\pi /4)c] = 1[/tex]

don't really seem to help me.

What am I missing?

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# Homework Help: Differentiation Question

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