Use this to find the equation of the tangent line to the curve y=5−3x^3 at the point (3−76) and write your answer in the form:

y=mx+b, where m is the slope and b is the y-intercept.

Question

Use this to find the equation of the tangent line to the curve y=5−3x^3 at the point (3−76) and write your answer in the form:
 
y=mx+b, where m is the slope and b is the y-intercept.

anonymous · Answer

could you help me @satellite73

anonymous · Answer

so, a derivative is only an equation to give you the tangent (aka. slope) of a a line at a particular point. In your y=mx+b equation, we need exactly such a slope... so we find the derivative of your equation:
$$\frac{d}{dx} (5-3x^{3}) = -9x^{2}$$

okay, so in order to determine the slope of the equation at your point (3, -76), you just need the x-coordinate!

Okay, so we have a slope m in our equation y=mx+b. What do we need to determine b? Well, we need a value for x and a value for y... aren't those two value part of a coordinate? I think we have what we need to determine the value for b, and therefore determine the equation for the tangent line!  : )

anonymous · Answer

$$m = -9(3)^{2}$$
$$m = -81$$

therefore
$$y=-81x+b$$
sub in our point:
$$-76=-81(3) + b$$
$$b=167$$
therefore:
$$y=-81x+167$$

anonymous · Answer

THANKS!!!