### Video Transcript

If the function π is such that π
of π₯ is equal to five π₯ minus three, then the variation function π of β is equal
to what at π₯ is equal to two.

We want to find the variation
function π of β for π of π₯ is five π₯ minus three at π₯ is equal to two. To do this, we recall that the
variation function for a function π of π₯ at π₯ is equal to π is defined as π of
β is π of π plus β minus π of π, where β is the change in π₯. In our case, our initial point π₯
is equal to two, and thatβs π, so that our variation function π of β is π of two
plus β minus π of two. Now, substituting first π₯ is equal
to two plus β into our function π, we have π of two plus β is five times two plus
β minus three, that is, 10 plus five β minus three, which is seven plus five β.

Next, if we substitute π₯ is equal
to two into our function π of π₯, we have π of two is five times two minus three,
which is 10 minus three, and thatβs seven. With these values in our variation
function, this gives us π of β is seven plus five β minus seven. And since seven minus seven is
zero, thatβs equal to five β. The variation function π of β for
the function π of π₯ is five π₯ minus three at π₯ is equal to two is therefore π
of β is equal to five β.