Question

Find all the value(s) of x at which f(x) = 3x3 + 15x2 + 26x – 2 has a horizontal tangent line. Select all correct answers. Select all that apply:

a. -5 b. -1 c. -5/3
d. 5 e. There are no values with a horizontal tangent.

Answer 1

To find the values of x at which f(x) = 3x^3 + 15x^2 + 26x - 2 has a horizontal tangent line, take the derivative of f(x), set it equal to 0, and solve for x.

Step-by-step explanation:

To find the values of x at which f(x) = 3x^3 + 15x^2 + 26x - 2 has a horizontal tangent line, we need to find the points where the derivative of f(x) is equal to 0. Taking the derivative of f(x), we get f'(x) = 9x^2 + 30x + 26. Setting f'(x) = 0 and solving for x, we find two values: x = -5/3 and x = -1. Therefore, the correct options are c. -5/3 and b. -1.

Answer 2

The function has real values of x at b. -1 and c. -5/3 at which it has a horizontal tangent line.

Step-by-step explanation:

To find the values of x at which the function f(x) = 3x^3 + 15x^2 + 26x - 2 has a horizontal tangent line, we need to find the points where the derivative of the function is equal to 0. Taking the derivative of f(x), we get:

f'(x) = 9x^2 + 30x + 26

Setting f'(x) = 0 and solving for x, we get:

`9x^2 + 30x + 26 = 0`

Dividing both sides by 3, we get:

`3x^2 + 10x + 8.6667 = 0`

Using the quadratic formula, we get:

`x = (-10 +\sqrt{(10^2 - 4(3)(8.6667))) / (2(3))`

`x = (-10 + \sqrt(28.1111)) / 6`

x = (-10 ± 5.3017) / 6

x = -2.2161 or x = -1.4849

Therefore, the correct options are b. -1 and c. -5/3