The slope of the the tangent line to a curve at a point. calc derivative

y = 108x + 216

Step-by-step explanation:

given

y = 4x³ then = 12x² =

x = 3 ⇒ m = 12(- 3)² = 108

equation of tangent in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept ), hence

y = 108x + b

To find b substitute (- 3, - 108) into the equation

- 108 = -324 + b ⇒ b = - 108 + 324 = 216

y = 108x + 216 ← equation of tangent

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

the answer is the third / last answer

step-by-step explanation: