The portal has been deactivated. Please contact your portal admin.

# Question Video: Finding the Variation Function at a Point for a Given Linear Function Mathematics

If the function π : π(π₯) = 5π₯ β 3, then the variation function π(β) = οΌΏ at π₯ = 2.

01:23

### 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 thatβs 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 thatβs 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, thatβs 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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.