(c) The line with equation y = 2x +k is a tangent to curve y = 3x² +4. Find the value of k.​

k = 11/3

Step-by-step explanation:

If the line is tangent to the curve, then Δ = 0.

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Remembering:

Δ>0 two different points of intersection x' x''

Δ=0 one point of intersection x' = x''

Δ<0 two different points of intersection in the complex plan x' and -x'

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As the line and the curve have one point of intersection, which is (x, y), we can make a equality between them:

2x + k = 3x² + 4

0 = 3x² - 2x + (4 - k)

Now we can use the Δ=0 (Δ= b² - 4ac)

Δ = 0 = (-2)² - 4.3.(4-k)

0 = 4 - 48 + 12k

12k = 44

k = 44/12 = 2 . 22 /3. 2.2 = 22/3.2 = 11/3

k = 11/3

d

step-by-step explanation: