1.

Let f(x) be a differentiable and g(x) be a twice differentiable function such that |f(x)-1|le1 and f^(')(x)=g(x). If f^(2)(3)+g^(2)(3)=20 then number of value(s) of cepsilon(0,4) such that g(c)g^('')(c)gt0 is/are _________

Answer»


Solution :`:' 0 LE f(x)le2`
and `g(3) epsilon [-2sqrt(5), -4]uu[4,2sqrt(5]`
Also `int_(0)^(4)g(x)dx=int_(0)^(4)f^(')(x)dx(f(4)-f(0) in(-2,2))`
Case I: Let `g(x) gt0` and `g^('')(x)gt0`
Clearly `int_(0)^(4)g(x)dx le` Area (MDKS)`=4`
Which is a contradiction
THUS, there is no such `C`
Similarly case II: Let `g(x)LT0` and `g^('')(x)lt0`


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