Write the equation of the line tangent to the curve at the point .

Question

Write the equation of the line tangent to the curve  at the point  .

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to take the derivative of the curve and evaluate it at the point given.

The derivative of the curve 11ea984b_b1d5_817d_9029_3513b0b674c1_TB4005_11 is:
y' = 2x - 4

Evaluating y' at the point 11ea984b_b1d5_a88e_9029_4f15e9da274e_TB4005_11 (x=3) gives:
y' = 2(3) - 4 = 2

So the equation of the tangent line at that point is:
y - y1 = m(x - x1)
y - 10 = 2(x - 3)
y - 10 = 2x - 6
y = 2x + 4

Converting this equation to the required format gives:
Answer: D
 The equation of the tangent line is y = 2x + 4.

Write the Equation of the Line Tangent to the Curve