Spruce budworms are a major pest that defoliates balsam fir. They are preyed upon by birds. A model for the per capita predation rate is given by f(N)=aNk2+N2 where N denotes the density of spruce budworms and a and k are positive constants. Find f′(N), and determine when the per capita predation rate is increasing and when it is decreasing.

f'(N) = a(k² - N²)/(k² + N²)

The function increases in the interval

(-k < N < k)

And the function decreases everywhere else; the intervals given as

(-∞ < N < -k) and (k < N < ∞)

Step-by-step explanation:

f(N)=aN/(k²+N²)

The derivative of this function is obrained using the quotient rule.

Then to determine the intervals where the function is increasinumber and decreasing,

The function increases in intervals where f'(N) > 0

and the function decreases in intervals where f'(N) < 0.

This inequality is evaluated and the solution obtained.

The solution is presented in the attached image.

Hope this Helps!!!

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

hard

step-by-step explanation: