Applications of Derivatives
Maxima Minima
MMTS_Full_Test_07
Grade 12
Question:
If $x_1$ and $x_2$ are the abscissae of the two points on $y=x(1-x^2)$ at which tangent lines are parallel to the chord joining $(1,0)$ and $(-1,0)$, then $x_1^2+x_2^2=$
$\dfrac{1}{2}$
$\dfrac{1}{3}$
$\dfrac{2}{3}$
$\dfrac{5}{3}$
Step-by-Step Solution
Key Concept: Slope of chord $=0$; find $x$ where $f'(x)=0$
$f'(x)=1-3x^2=0\Rightarrow x^2=1/3$. $x_1^2+x_2^2=2/3$.
Correct Answer: 1