SMALL INCREMENTS FORMULA + IMPLICIT DIFFERENTIATION+ TUTORIAL 3- UTILITY FUNCTIONS

A curve has the equation y=2x^3 +3x^2 -12x. Use small increments formula to estimate changes in Y when X changes from i) 2 to 1.99 ii) 2 to 2.01. show working

check notes, answers should be -0.24 and 0.24. firstly differentiate, then put y= 2 into eq. then times by 0.01 to find difference (0.24)

use answer from a) to estimate the value of y when x = 1.99 and 2.01

check notes for method, answer is 3.76 and 4.24

IMPLICIT DIFF: find dy/dx if 8y^3 + 2x^2y - x = 60

check notes: -4xy-1/ 24y^2 + 2x^2

Whats the equation for marginal rate of substitution?

\- MUx/ MUy or -MU1/MU2

When we divide powers this is the same as…

minusing powers, e.g. x^8/x^5= x^3

How do we check the law of diminishing utility

we differentiate twice, if the answer is less than zero then law of diminishing marginal utility holds. if it is above 0 then law of diminishing marginal utility doesn’t hold

calculate the marginal utility from this utility function: u(x,y) = x^2/3y^4/5. then find law of diminishing returns for MUx and MUy. then calculate MRS

check tutorial 3 answers