Find an equation of the tangent line at the given value of x. , x = 3
A) y = 2x + 6
B) y = 2x - 6
C) y = 3x - 9
D) y = 3x + 9

Question

Find an equation of the tangent line at the given value of x.  , x = 3
A) y = 2x + 6 
B) y = 2x - 6 
C) y = 3x - 9 
D) y = 3x + 9

Quizplus · Accepted Answer

To find the equation of the tangent line at x = 3, we need to take the derivative of the function at x = 3 and plug it into the point-slope formula. 
Given function: 2x^2 - 3x - 3
Derivative: 4x - 3
At x = 3, the derivative is 4(3) - 3 = 9
Using the point-slope formula with the point (3, -12) and slope 9, we get:
y - (-12) = 9(x - 3)
Simplifying, we get y = 9x - 39, which is in the form of y = mx + b. Therefore, the correct answer is option C: y = 3x - 9.

Find an Equation of the Tangent Line at the Given