Answer:
To find the second derivative \( h''(x) \) for the function \( h(x) = 3x - 5 - 6x^7 \), we need to differentiate the function twice with respect to \( x \).
First, let's find the first derivative \( h'(x) \) of \( h(x) \):
\[ h'(x) = \frac{d}{dx}(3x - 5 - 6x^7) \]
\[ h'(x) = 3 - 42x^6 \]
Now, let's find the second derivative \( h''(x) \) by differentiating \( h'(x) \) with respect to \( x \):
\[ h''(x) = \frac{d}{dx}(3 - 42x^6) \]
\[ h''(x) = 0 - 6 \cdot 42x^5 \]
\[ h''(x) = -252x^5 \]
So, the second derivative \( h''(x) \) for the function \( h(x) = 3x - 5 - 6x^7 \) is \( -252x^5 \).
