### Calculus Problem: Find the Second DerivativeGiven:\[ h(x) = (10 - x^2)(5x + 17) \]we are asked to find the second derivative of the function \( h \).First, determine the first derivative \( h'(x) \).\[ h'(x) = \frac{d}{dx}[(10 - x^2)(5x + 17)] \]To find \( h'(x) \), we need to use the product rule, which states:\[ \frac{d}{dx}[u \cdot v] = u' \cdot v + u \cdot v' \]where \( u = (10 - x^2) \) and \( v = (5x + 17) \).Next, find the first derivative of each function:\[ u = 10 - x^2 \quad \Rightarrow \quad u' = -2x \]\[ v = 5x + 17 \quad \Rightarrow \quad v' = 5 \]Apply the product rule:\[ h'(x) = (-2x)(5x + 17) + (10 - x^2)(5) \]\[ h'(x) = -10x^2 - 34x + 50 - 5x^2 \]\[ h'(x) = -15x^2 - 34x + 50 \]Now, we find the second derivative \( h''(x) \), which is the derivative of \( h'(x) \):\[ h''(x) = \frac{d}{dx}(-15x^2 - 34x + 50) \]\[ h''(x) = -30x - 34 \]Thus, the second derivative of the function \( h \) is:\[ h''(x) = -30x - 34 \]

Name: ### Calculus Problem: Find the Second DerivativeGiven:\[ h(x) = (10 -
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Calculus Problem: Find the Second DerivativeGiven:\[ h(x) = (10 - x^2)(5x + 17) \]we are asked to find the second derivative of the function \( h \).First, determine the first derivative \( h'(x) \).\[ h'(x) = \frac{d}{dx}[(10 - x^2)(5x + 17)] \