Consider the equation below. f(x) = 4x3 + 15x2 − 150x + 9 (a) find the intervals on which f is increasing. (enter your answer using interval notation.)

Increasing on (-∞, -5) and (2.5, ∞)

Step-by-step explanation:

ƒ(x) = 4x³ + 15x² - 150x + 9

Step 1.Find the zeros of the first derivative of the function

ƒ'(x) = 12x² + 30x -150 = 0

             2x² + 5x - 25 = 0

             (x + 5)(2x - 5) = 0

               x = -5 or x = 2.5

These are your critical points.

Step 2. Apply the first derivative test.

Test all intervals to the left and to the right of these values to determine if the derivative is positive or negative.

(a) x = -10

ƒ'(-10) = 12(-10)² + 30(-10) - 150 = 1200 - 300 - 150 = 750

ƒ'(x) > 0 so the function is increasing on (-∞, -5).

(b) x = 0

ƒ'(0) = 12(0)² + 30(0) -150 = -150  

ƒ'(x) < 0 so the function is decreasing.

(c) x = 10

ƒ'(0) = 12(10)² + 30(10) -150 = 1200 + 300 - 150 = 1350  

ƒ'(x) > 0 so the function is increasing on (2.5, ∞).

The function is increasing on (-∞, -5) and (2.5, ∞).

step-by-step explanation:

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !