00:01
The percentage of normal consumption of pure per pune, that is anna of f, is given by the root of 9 ,000 negative 38 negative 0 .03 x square.
00:20
Where x is the percentage of luxury tax.
00:34
In first a part, we need to find rate of change of.
00:39
T n over t x so differentiate the n with expect to x if this is equal to t over d x of root of 9 000 negative 30 x negative 0 .03 x squared but as we know that derivative of root x is equal to 1 over twice of 2 x therefore this is equal to 1 over 2 of root of 9 ,000 negative 30x negative 0 .03 square appaligned the chain rule d over dx of 9 ,000 negative 38 negative 0 .038 so this is equal to negative sorry is equal to negative 30 negative 0 .06 x over 12 of root of 9 ,000 negative 30s negative 0 .02 so it implies tn over t x is equal to negative negative 0 .03x over root of 9 ,000, 30s negative, 0 .036.
02:36
Therefore, the rate of change of n, that is a billion over tx, is equal to negative, 15 plus 0 .03x over root of 9 ,000, negative 30x negative 0 .03 so this is our required final answer.
03:12
Now in part b, we find the rate of change of n, tn over dx, at x is equal to 110.
03:29
So substitute x is equal to 110 in case of x...
