00:01
The question is, estimate using the linear approximation and find the error using a calculator.
00:06
And the expression we're given is 16 .5 to the 1 fourth minus 16 to the 1 fourth.
00:13
So looking at this expression, we can see that f of x is equal to x to the 1 fourth, where a equals 16 and delta x equals 0 .5.
00:48
So now if we want to use the linear approximation, which is given right here, we need to find the derivative of f at point a multiplied by delta x.
01:00
So we can go ahead and find the derivative of f of x, and we can do that with the power rule.
01:13
So the derivative of x to the one -fourth would be you bring down the one -fourth, and you subtract one on the exponent, giving you negative three -fourths.
01:32
And now to find the derivative at point a, you'll just need to plug in 16 for x, and that gives you 1 over 32...