MathematicsIf F(x)=f(x)g(x)h(x) for all real x, where f(x),g(x)and hx are differentiable functions at some point x0If F|(x0)=21F(x0),f|(x0)=4f(x0),g|(x0)=−7g(x0) and h'(x0)=kh(x0), then k=

If $F (x) = f (x) g (x) h (x)$ for all real $x$ , where $f (x), g (x)$ and $h (x)$ are differentiable functions at some point $x_{0}$ If $F^{|} (x_{0}) = 21 F (x_{0}), f^{|} (x_{0}) = 4 f (x_{0}), g^{|} (x_{0}) = - 7 g (x_{0})$ and $h' (x_{0}) = k h (x_{0})$ , then $k =$

A
22
B
26
C
28
D
24

Solution:

$F (x) = f (x) g (x) h (x) \forall x \in R$

$F^{|} (x) = f^{1} (x) g (x) h (x) + f (x) g^{|} (x) h (x) + f (x) g (x) h^{|} (x)$

$at x = x_{0}$

$F^{|} (x_{0}) = f^{1} (x_{0}) g (x_{0}) h (x_{0}) + f (x_{0}) g^{|} (x_{0}) h (x_{0}) + f (x_{0}) g (x_{0}) h^{|} (x_{0})$

$21 F (x_{0}) = 4 f (x_{0}) . g (x_{0}) h (x_{0}) - 7 f (x_{0}) g (x_{0}) h (x_{0}) + k . h (x_{0}) f (x_{0}) g (x_{0})$

$21 = 4 - 7 + k [∵ F (x_{0}) = f (x_{0}) . g (x_{0}) h (x_{0})]$

$\Rightarrow k = 24$

Solution:

Related content