Determine whether the following polynomials are decreasing or increasing over the interval?

Question

1. F(x) = 3x^3 - 7x^2 + x - 8
2. F(x) = -5x^5 + 9x^3 + 4x^2 + 23
3. F(x) = x^4 + x^3 + x^2 + x + 1
4. F(x) = 5x^2 + 25x + 30

Answer 1

you need to find the first Derivative of the function and set that to 0 which is where the function is neither increasing or decreasing. Then evaluate the value of the derivative on each side of the solution. if it is + the function is increasing and if it is negative the function is decreasing

3x^3-7x^2+x-8 The first derivative is 9x^2 -14x +1 Now set this equal to zero and solve

will need to solve with quadratic formula and will get x= 1.48 and x=.075

so need to evaluate at x<.075 x>1.48 and x between these 2 values

at f(0) =+1

f(1)= -4

f(2)=+23

so the function increases at x>.075 decreases between 0.075 and 1.48 and increases at x>1.48

You can use the same technique to evaluate the other functions