Calc .....SLOPE HELP!!?

Question

What is the maximum slope of the tangent to the curve y = –x3 + 3x2 + 9x – 27?

Answer 1

First you have to find the derivative:

y' = -3x^2 + 6x + 9

One of the y values in the range of the above equation will be your slope. In order to find the max value, calculate the second derivative:

y'' = -6x + 6 = -6(x-1)
+ 1 -
---|----

You will have the maximum slope when x = 1.

y' = -3(1)^2 + 6(1) + 9 = -3 + 15 = 12

The maximum slope = 12.

Answer 2

First, you ought to take the spinoff, and then replace in 2 for x to locate the slope of the tangent at that distinctive element. f(x) = 3(x + a million)^-a million we are going to use the chain rule, letting u = (x + a million). Then, as quickly as we differentiate the functionality with u, we multiply the spinoff of the functionality f(u) with the spinoff of u = x + a million, that's one, so we don't ought to somewhat complication approximately it, using fact one does not replace something. f(x) = 3u^-a million f best (x) = -3u^-2 situations u best (that's only one, using fact the spinoff of x + a million is one) f best (x) = -3/(x + a million)^2 f best (2) = -3 (2 + a million)^2 f best (2) = -3/9 f best (2) = -a million/3 f best (x) represents the spinoff of f(x), btw.

Answer 3

dy/dx = -6x² + 6x + 9
Since this has no bound as x -> ± ∞ there is no 'maximum' slope. It increases in the negative direction without bound.

Doug

Answer 4

Wow girl are you taking some AP calculas? Damn I hate math with a passion.