Find the equation of the tangent line to the graph g(x)

Question

at the point x=2 g(x)= 3x^2-4x?

Answer 1

The curve g(x) = 3x² - 4x

y = 3x² - 4x

Differentiating  on each side with respect to x.

y' = 6x - 4

Substitute the values x  = 2 in above equation.

y' = 6(2) - 4

y' = 8

This is slope(m) of the tangent line.

m = 8.

Using the x - value find the corresponding y - value with the curve.

y = 3(2)² - 4(2)

y = 12 - 8 = 4

Tangent point is (x, y) = (2 , 4)

To find the tangent line equation, substitute the values of m = 8 and (x, y) = (2, 4)  in the slope intercept form of an equation y = mx + b.

4 = 8(2) + b

4 - 16 =  b

b = - 12

Substitute the values m = 8 and b = - 12 in y = mx + b

y = 8x - 12

Equation of tangent line is y = 8x - 12.