To find h'(2), apply the product rule of differentiation to get h'(2) = f'(2)g(2) + 7g'(2), expressed in terms of f(x) and g(x).
To evaluate h'(2), we need to use the product rule of differentiation, which states that if h(x) = f(x) · g(x), then h'(x) = f'(x)g(x) + f(x)g'(x). We are given that f(2) = 7.
Therefore, using the product rule, we have:
h'(2) = f'(2)g(2) + f(2)g'(2)
Substitute f(2) = 7 to obtain:
h'(2) = f'(2)g(2) + (7)g'(2)
This expression represents the value of h'(2) in terms of the original functions f(x) and g(x).
The probable question may be:
Consider the functions \(f(x)\) and \(g(x)\), where \(h(x) = f(x) \cdot g(x)\). Given that \(f(2) = 7\), evaluate \(h'(2)\), the derivative of \(h(x)\) with respect to \(x\), at \(x = 2\). Express the result in terms of the original functions \(f(x)\) and \(g(x)\).