Let f(x)=x3+3 x+2 and x=c be a point such that f'(c) ≠ (f(b)-f(a)/b-a) for any two values of a, b ∈ R , then number of such point is .

Question

Let f(x)=x3+3 x+2 and x=c be a point such that f'(c) ≠ (f(b)-f(a)/b-a) for any two values of a, b ∈ R , then number of such point is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For such points x=c, f''(c)=0 ∴ there is one point only

Q. Let $f (x) = x^{3} + 3 x + 2$ and $x = c$ be a point such that $f^{'} (c) \neq = \frac{f ( b ) - f ( a )}{b - a}$ for any two values of $a, b \in R$ , then number of such point is ___.

For such points $x = c, f^{''} (c) = 0$
$∴$ there is one point only

Q. Let f(x)=x3+3x+2 and x=c be a point such that f′(c)=b−af(b)−f(a)​ for any two values of a,b∈R, then number of such point is ___.

For such points x=c,f′′(c)=0 ∴ there is one point only

Q. Let $f (x) = x^{3} + 3 x + 2$ and $x = c$ be a point such that $f^{'} (c) \neq = \frac{f ( b ) - f ( a )}{b - a}$ for any two values of $a, b \in R$ , then number of such point is ___.

For such points $x = c, f^{''} (c) = 0$
$∴$ there is one point only