# Thread: Find values with tangent to a curve

1. ## Find values with tangent to a curve

Find the values of m for which the line y = mx - 9 is a tangent to the curve x^2 = 4y.

All I need is the basic formula? I can't find one anywhere.

2. differentiate both sides
$\frac{d}{dx}(x^2)=\frac{d}{dx}(4y)$

$2x=4\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{1}{2}x$

now $\frac{dy}{dx}$ would be the gradient of the curve (m in the formula)

substitute this in along with $y=\frac{1}{4}x^2$ (you are given this) into the equation of the line you want to find and solve this for x

I get

$x=\pm6$

now plug these values into your expression for $\frac{dy}{dx}$ to find the values of m (remember dy/dx=m)

3. Thank you so much

,

# y=mx-9 is tangent to the curve

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