Let y=f(x) be a twice differentiable function such that f(1)=2 ; f(2)=-1 ; f(3)=5 ; f(4)=- 3 and f(5)=1. Find the minimum number of real roots of the equation f prime(x) ⋅ f prime prime(x)=0.

Question

Let y=f(x) be a twice differentiable function such that f(1)=2 ; f(2)=-1 ; f(3)=5 ; f(4)=- 3 and f(5)=1. Find the minimum number of real roots of the equation f prime(x) ⋅ f prime prime(x)=0. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f (x) = 0 has atleast 4 real roots (IMVT) f '(x) = 0 has atleast 3 real roots (Rolle's) f "(x) = 0 has atleast 2 real roots (Rolle's)

Q. Let $y = f (x)$ be a twice differentiable function such that $f (1) = 2; f (2) = - 1; f (3) = 5; f (4) = -$ 3 and $f (5) = 1$ . Find the minimum number of real roots of the equation $f^{'} (x) \cdot f^{''} (x) = 0$ .

$f (x) = 0$ has atleast 4 real roots (IMVT)
$f^{'} (x) = 0$ has atleast 3 real roots (Rolle's)
$f " (x) = 0$ has atleast 2 real roots (Rolle's)

Q. Let y=f(x) be a twice differentiable function such that f(1)=2;f(2)=−1;f(3)=5;f(4)=− 3 and f(5)=1. Find the minimum number of real roots of the equation f′(x)⋅f′′(x)=0.

f(x)=0 has atleast 4 real roots (IMVT) f′(x)=0 has atleast 3 real roots (Rolle's) f"(x)=0 has atleast 2 real roots (Rolle's)

Q. Let $y = f (x)$ be a twice differentiable function such that $f (1) = 2; f (2) = - 1; f (3) = 5; f (4) = -$ 3 and $f (5) = 1$ . Find the minimum number of real roots of the equation $f^{'} (x) \cdot f^{''} (x) = 0$ .

$f (x) = 0$ has atleast 4 real roots (IMVT)
$f^{'} (x) = 0$ has atleast 3 real roots (Rolle's)
$f " (x) = 0$ has atleast 2 real roots (Rolle's)