Alan

Deleted. Misinterpreted the question!

There are three turning points, so you have a fourth order polynomial.  It has roots at -5 and -1 (i..e. places where the function is zero.

Write the function as f(x) = -(x + 5)(x + 1)(x - a)(x - b)  where a and b are to be found (the initial negative sign is because the function goes to -infinity as x goes to +/- infinity)

When x = 0 we have f(0) = -25, so    -5*a*b = -25  ...(1)

There gradient of f is zero when x = -3, so differentiate f with respect to x and set the result equal to zero (with x = -3)

df/dx = -(4*x^3 + (18-3a-3b)*x^2 + (2ab-12a-12b+10)*x - 6ab - 5a -5b) 

so 4*(-3)^3 + (18 - 3a - 3b)*(-3)^2 + (2ab -12a -12b + 10)*(-3) -6ab - 5a -5b = 0   ...(2)

You now have two equations for the two unknowns a and b.

Can you take it from here?

I think you mean f(x)^16 rather than f(x)16.  This question has been asked and answered several times.  Search the Answers for the solution.

"Triangle ABC has vertices A (0,0), B (0,3), C(5,0). A point  inside the triangle is  sqrt 10 units from point  A and sqrt 13 units from point B. How many units is P from point C? Express your answer in simplest radical form."

time = distance/speed

speed in still water = v

net speed upstream = v - 5

net speed downstream = 5 + v

So:  2/(v-5) = 12/(5 + v)

Can you take it from here? 

Like so

Like so:

I assume you know the Laplace transform of y`, y and a constant, and the inverse transform of 1/s and 1/(s+constant):

Think of it like this:

(1*7 + 1)/7           8

(2*7 + 2)/7          16

(3*7 + 3)/7          24

(4*7 + 4)/7          32

(5*7 + 5)/7          40

(6*7 + 6)/7          48

Rewrite the inequality as

x^2 - 4x + y^2 - 6y ≤ 13

x^2 - 4x + 4 + y^2 - 6y + 9 = 13 + 4 + 9

(x-2)^2 + (y - 3)^2 ≤ 26

This is the area of a circle centred on x = 2, y = 3, with a radius of r = √26.

I'll leave you to find the area of a circle with radius r = √26.