Consider the functiony = 3x^5 - 25x^3 + 60x+ 1. Use the first derivative test to decide whether this function has a maximum at x = 1. Which of the following describes what you found? A. The derivative is positive to the left of x = 1 and positive to the right of x = 1, so the function has neither a relative maximum nor a minimum at x = 1.

B. None of these apply

C. The derivative is negative to the left of x = 1 and positive to the right of x = 1, so the function has a relative minimum at x = 1.

D. The derivative is positive to the left of x = 1 and negative to the right of x = 1, so the function has a relative maximum at x = 1.

E. The derivative is positive to the left of x = 1 and negative to the right of x = 1, so the function has a relative minimum at x = 1.

Option A

Step-by-step explanation:

Expression for the given function is,

y = 3x⁵ - 25x³ + 60x + 1

First derivative of the given function will be,

y' = 15x⁴ - 75x² + 60

For the critical points of the function,

y' = 0

15x⁴ - 75x²+ 60 = 0

x = 1

On the left side of x = 1,

Let x = 0

y' = 15(0)⁴ - 75(0)²+ 60

y = 60 [Positive]

On the right side of x = 1,

Let x = 3

y' = 15x⁴ - 75x²+ 60

y' = 15(3)⁴ - 75(3)² + 60

y' = 1215 - 675 + 60

y' = 600 [Positive]

Since, the derivative is positive on both the sides of x = 1,

Function will have neither maximum neither minimum at x = 1.

Option A is the answer.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3