A function f is defined as f(.x.)=(k - x2 + 3 x/- 4 + x) where k is a parameter, Then the greatest integral value of k so that function f has a relative minimum and a relative maximum is:

Question

A function f is defined as f(.x.)=(k - x2 + 3 x/- 4 + x) where k is a parameter, Then the greatest integral value of k so that function f has a relative minimum and a relative maximum is: (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)=(-x2+3 x+k/x-4) f prime(x)=((-2 x+3)(x-4)--x2+3 x+k/(x-4)2) f prime(x)=0 Leftrightarrow-x2+8 x-12-k=0 Leftrightarrow x2-8 x+12+k=0 ...(i) f has a relative minimum and a relative maximum ⇒ Equation (i) has real and distinct roots Leftrightarrow Discriminant of i>0 Leftrightarrow 64-4(12+k)>0 Leftrightarrow k< 4 ⇒ The greatest integral value of k=3.

Q. A function f is defined as f(x)=−4+xk−x2+3x​ where k is a parameter, Then the greatest integral value of k so that function f has a relative minimum and a relative maximum is:

Q. A function $f$ is defined as $f (x) = \frac{k - x ^{2} + 3 x}{- 4 + x}$ where $k$ is a parameter, Then the greatest integral value of $k$ so that function $f$ has a relative minimum and a relative maximum is: