Question

Help find the tangent line?

Answer 1

The function f(x) = x² + 4x - 4

f(1) = (1)² + 4(1) - 4

= 1 + 4 - 4

= 1

f(x) = x² + 4x - 4

Differentiating  on each side with respect of x .

y' = 2x + 4

Substitute the values (x , y) = (1,1) in above equation.

y' = 2(1) + 4

= 6

This is the slope of tangent line to the curve at (1, 1).

To find the tangent line equation, substitute the values of m = 6 and (x, y ) = (1, 1).  in the slope intercept form of an equation y = mx + b.

1 = 6(1) + b

1 - 6 = b

b = - 5

Substitute m = 6 and b = - 5 in y = mx + b.

The equation of tangent line is y = 6x - 5.