Question

The diagram shows the curve y=(4-x)^ex and its maximum point M. the curve cuts the x-axis at A and the y-axis at B
write down the co-oordinates of A and B
Find the x-coordinate of M
The point P on the curve has x-coordinates of P the tangent to the curve at P passes through the origin O calculate the value of p(the x-coordinate).

Answer 1

Question 18 i solved part 1 i got the coordinates of A and B

Answer 2

First, you mean
the curve y=(4-x) e^x (not y=(4-x)^ex)

M looks like the peak of the curve, where the slope of the curve is "flat" (i.e. zero)

find dy/dx and set it equal to zero. solve for x

Answer 3

for point P, we use this idea:



the slope is also the derivative