Use the given information to find f '(4).
f(x) = 5g(x) + h(x)
g(4) = -4 and g'(4) = 6
h(4) = 1 and h'(4) = -5
f '(4) = ?
To find f '(4), we need to use the information about the derivatives of g(x) and h(x) as well as the function f(x).
Given:
f(x) = 5g(x) + h(x)
g(4) = -4 and g'(4) = 6
h(4) = 1 and h'(4) = -5
First, let's find the derivative of f(x) with respect to x:
f'(x) = 5g'(x) + h'(x)
Since we are interested in f '(4), we substitute x = 4 into the equation:
f'(4) = 5g'(4) + h'(4)
Now we substitute the given values:
f'(4) = 5(6) + (-5)
Performing the calculations, we have:
f'(4) = 30 - 5
The final answer is:
f'(4) = 25