Is there an error in this problem?

[madsmh]

I am currently working on problem 32-15 in Calculus by Spivak, and in question (b)

in the bottom line there is a relation
$[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]+[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0$

But I can only get it to work out if

$[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]-[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0$

as this would make sense since

Spoiler

$\int_a^b \phi_1''(x)\phi_2(x)-\phi_2''(x)\phi_1(x) + \phi_1'(x)\phi_2'(x)-\phi_1'(x)\phi_2'(x) dx = \int_a^b (\phi_1'(x)\phi_2(x))' dx - \int_a^b (\phi_2'(x)\phi_1(x))' dx$

which would make it natural to conclude that the relation above is >0, since the above integral has been shown to be >0.

.. Mads

 

[SammyS]

I hard to guess what's going on here.

What is the problem as stated in the textbook, and where are you stuck?