Question

The area bounded by the tangent on the curve
$y=4x^2+2x\text{at (0, 0)},y-10=-x\text{and}y=0$ is

• A. $\frac{100}{9}\text{sq.units}$
• B. $20\text{sq.units}$
• C. $\frac{100}{3}\text{sq.units}$
• D. $\frac{200}{9}\text{sq.units}$

Answer 1

The correct option is C $\frac{100}{3}\text{sq.units}$

$y=4x^2+2x\Rightarrow y^{\prime }=8x+2\Rightarrow y^{\prime }{|}_{x=0}=2$
Equation of the tangent on the parabola at $(0,0)$
$y=2x$


Point of intersection of tangent and the given line,
$2x=10-x\Rightarrow x=\frac{10}{3}\Rightarrow y=\frac{20}{3}$
Coordinates of $A=(\frac{10}{3},\frac{20}{3})$
So the area bounded $=$ area of $△OAB$
Area $=\frac{1}{2}\times \frac{20}{3}\times 10=\frac{100}{3}\text{sq.units}$