Question

Y=k is a tangent to
y = x² + 2x. Find the value(s) of k.

Answer 1

k=−1

The point of contact is:

(0,−1)

Step-by-step explanation:

Compute the first derivative of the curve:

dyd x=2−2x

The slope of the line is 2, therefore, we set the first derivative equal to 2 and then solve for x:

2=2−2x

x=0←

this is the x coordinate of the point of contact.

The y coordinate of the point of contact is found by evaluating the function at x = 0:

y=−1+2

(0)

−02

y=−1←

this is the y coordinate of the point of contact.

The point of contact is:

(0,−1)

Find the value of k by evaluating the line at the point of contact:

−1=2

(0+k

k=−1

Step-by-step explanation: