How many real solutions does the equation `x^7+14 x^5+16 x^3+30 x-560=0` have?

Options

A. 1
B. 3
C. 5
D. 7

Explanation

To determine how many real solutions the equation \( x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 \) has, we can follow these steps:

### Step 1: Define the function
Let \( f(x) = x^7 + 14x^5 + 16x^3 + 30x - 560 \).

### Step 2: Find the derivative
To analyze the behavior of the function, we need to find its derivative:
\[
...