Question
Question: Let F(x) = f(x) g(x) h(x) for all real x where f(x), g(x) and h(x) are differentiable functions. At ...
Let F(x) = f(x) g(x) h(x) for all real x where f(x), g(x) and h(x) are differentiable functions. At some point
x0, F ' (x0) = 21 F (x0), f ' (x0) = 4 f (x0)
g ' (x0) = – 7 g(x0), h ' (x0) = k h' (x0), then k =
A
24
B
12
C
0
D
21
Answer
24
Explanation
Solution
F ' (x) = f ' (x) g (x) h (x) + f (x) g'(x) h(x) + f(x) g(x) h ' (x)
21 F(x0) = 4 f(x0) g(x0) h(x0) – 7f(x0)
g(x0) h(x0)+ f(x0) g(x0) kh(x0)
21 F(x0) = (k – 3) f(x0) g(x0) h(x0)
(Q F(x0) = f(x0) g(x0) h(x0))
21 = k – 3
k = 24