A differentiable function y=f(x) is such that its graph cuts the curve y=a x2+b x+c at 10 distinct points. Find the minimum number of distinct roots of f prime prime prime( x )=0.

Question

A differentiable function y=f(x) is such that its graph cuts the curve y=a x2+b x+c at 10 distinct points. Find the minimum number of distinct roots of f prime prime prime( x )=0. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

O MR Let g(x)=f(x)-(a x2+b x+c). text Since, g(x)=0 text has 10 text distinct real roots, ⇒ g prime(x)=0 text has minimum 9 text distinct real roots, ⇒ g prime prime(x)=0 text has minimum 8 text distinct real roots, ⇒ g prime prime prime(x)=0 text has minimum 7 text distinct real roots, ⇒ f prime prime prime(x)=0 text has atleast 7 text distinct real roots. Ar

Q. A differentiable function y=f(x) is such that its graph cuts the curve y=ax2+bx+c at 10 distinct points. Find the minimum number of distinct roots of f′′′(x)=0.

O MR Let g(x)=f(x)−(ax2+bx+c). Since, g(x)=0 has 10 distinct real roots, ⇒g′(x)=0 has minimum 9 distinct real roots, ⇒g′′(x)=0 has minimum 8 distinct real roots, ⇒g′′′(x)=0 has minimum 7 distinct real roots, ⇒f′′′(x)=0 has atleast 7 distinct real roots. Ar

Q. A differentiable function $y = f (x)$ is such that its graph cuts the curve $y = a x^{2} + b x + c$ at 10 distinct points. Find the minimum number of distinct roots of $f^{'''} (x) = 0$ .