Derivative Applications--word problem

[volgirl89]

"The average pollen count in New York City on day 'x' of the pollen season is P(x)=8x-0.2x^2 (for 0<x<40). On which day is the pollen count highest?"
The answer is on the 20th day

Here's my work:
I took the derivative. Then I plugged -200 into the original equation and got -2400... What am I not doing?
P'(x)= 8+4x
= .04(200+x)=0
x= -200

 

[wjm11]

The average pollen count in New York City on day 'x' of the pollen season is P(x)=8x-0.2x^2 (for 0<x<40). On which day is the pollen count highest?"
The answer is on the 20th day

Here's my work:
I took the derivative. Then I plugged -200 into the original equation and got -2400... What am I not doing?
P'(x)= 8+4x

No,
P'(x) = 8 - .4x = 0

x = 8/.4 = 20

The day on which the pollen count is highest is day 20. Plug 20 in for x to find the pollen count.

Note: you can also double check your work by graphing this equation. Remember also that the vertex of the parabola is on the axis of symmetry, x = -b/2a.