Find an equation of the tangent line to the graph of the function f defined by the equation at the indicated point.

Question

Find an equation of the tangent line to the graph of the function f defined by the equation at the indicated point. ​  ​

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function and evaluate it at the given point. 
$f(x) = 3x^2 - 2x$ 
$f'(x) = 6x - 2$ 
When x = 1, 
$f'(1) = 6(1) - 2 = 4$ 
So the slope of the tangent line is 4. 
To find the y-intercept of the tangent line, we can use the point-slope form: 
$y - f(1) = m(x - 1) \implies y - 1 = 4(x - 1)$ 
Simplifying, we get: 
$y = 4x - 3$ 
Therefore, the equation of the tangent line at the point (1,1) is y = 4x - 3, which is choice C.

Find an Equation of the Tangent Line to the Graph