Help with a few questions (1 Viewer)

[^bindy^]

a) Determine the coordinates of the point(s) where the curve y=2x^2e^2x crosses the coordinate axes
b) differentiate the equation y=2x^2e^2x
c) hence find the coordinates of the stationary points on the curve y=2x^2e^2x, and determine their nature.

AND

Gareth currently has $100 000 in his superannuation fund, which pays 0.7% interest per month. When he retires in 8 yeras time, he will need $350 000. How much will he need to invest at the end of each month for the next 8 years so that he will have $350 000 when he retires?

thanks heaps in advance

 

[pLuvia]

a) Coordinate axis as in the x and y axis. Crosses the y axis when x=0, and crosses the x acis when y=0

b) Use product rule

c) When you get the differentiated equation, let that equal to 0, then solve for x. Then test either sides of the stationary points you have found to determine the nature of it

d) Use principle of equivalence
Let X be the amount deposited every month
100000(1.007)⁹⁶+X((1.007)+....+(1.007)⁹⁶)=3500000
100000(1.007)⁹⁶+X(1.007)[(1-(1.007)⁹⁶)/(1-1.007)]=350000

Then solve for X