Question

On the curve $y$ = $4x^2$ - 6x + 3 find the point at which the tangent is parallel to the straight line $y=2x$.

Answer 1

Since the tangent is parallel to $y=2x$, hence the slope of tangent is equal to the slope of this line.

Now equation of a line $y=mx+c$ has $m$ as its slope.

Hence slope of the given line is $2$

Now, for the curve $y=4x^2-6x+3$

Slope$=\frac{dy}{dx}=8x-6=2$

$⟹x=1$

At, $x=1$, $y=4-6+3=1$

Hence at $(1,1)$, the tangent to the curve is parallel to $y=2x$