Calculus question? Please?

Question

Find the slope of the tangent line to the parabola y 4x x 2 +5x + 4 at the point (-4,48) is: _______ 

The equation of this tangent line can be written in this form y = mx + b where m is: 
____ and where b is: _____

Answer 1

The curve parabola equation is y = 4x² + 5x + 4

Differentiating on each side with respect of x .

y' = 8x + 5

Substitute the values (x , y) = (-4, 48) in above equation.

y' = 8(-4) + 5

y' = - 32 + 5

y' = - 27

- 27 is the slope of tangent line to the parabola at (- 4, 48).

To find the tangent line equation, substitute the values of m = -27 and (x, y) = (-4, 48) in the slope intercept form of an equation y = mx + b.

Where m is slope and b is y intercept.

48 = - 27(- 4) + b

48 = 108 + b

b = 48 - 108

b = - 60

Substitute m = - 11 and b = -60 in y = mx + b.

y = - 27x - 60

Tangent line equation is y = - 27x - 60.

m = -27 and b =-60