The point at which the function $'f'$ given by $f(x)=(x-2)^4(x+1)^3$ has point of inflexion is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x=-1$
$f(x)=(x-2)^4(x+1)^3$
$f'(x)=4(x-2)^3(x+1)^3+3(x-2)^4(x+1)^2$
$=(x-2)^3(x+1)^2(7x-2)$
$f''(x)=(x-2)^2(x+1)(7x-2)(12x-15)$
for point of inflection, $f''(x)=0$
$(x+1)=0⇒x=-1$