GROVE PRELIM 2U/3U TEST YOURSELF 8 - Q15

QUESTION:

Find the equation of the tangent to the curve $y=x^2+2x-5$ that is parallel to the line $y=4x-1$.

SOLUTION:

We need to find the $x$ value on the curve at which the tangent has gradient $m=4$ 
(since the line $y=4x-1$ has gradient $4$)

Find $y'$.
 (since $y'$ is the gradient of the tangent at $x$)

$y'=2x+2$

Solve $y'=4$.

$2x+2=4$

$2x=2$

$x=1$

When $x=1$, $y=(1)^2+2(1)-5=-2$

So the point is $(1,-2)$.

Tangent has equation $y-y_1=m(x-x_1)$

$$y--2=4(x-1)$$

$$y+2=4x-4$$

$$4x-y-6=0$$