Find the equation of the normal to the curve at the given value of x.

answer:

explanation

the normal is perpendicular to the tangent. we need to find the slope of the tangent line to at and then take the negative reciprocal of that, which will give us a perpendicular slope to the tangent (the normal slope).

at x=-1, the y-coordinate is

so the point at which this normal occurs is (-1,-8).

to find tangent slope, we differentiate the curve with respect to x. we can use the power rule for differentiation, which says that :

the slope of the tangent at x = -1 is

so the normal slope is the negative reciprocal of that: 1/4.

with point-slope form of a line, , and knowing that this normal is at (-1,-8), the equation is

side note:

we can get an equivalent equation. if we distribute

and multiply both sides by 4 to get rid of denominator

and then isolate one side, we get

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !