Verified answer

Recall that the derivative of a function gives another function whose values are the slopes of the original function. Take the derivative of your function there with the chain rule:

f ' (x) = 2[2(5x + 1)^2 + 5] [20(5x + 1)]

Note that we took the derivative of [2(5x + 1)^2 + 5] with the chain rule as well. Now simply sub in x = -1 to find the slope at that point:

f ' (-1) = 2[2(5{-1} + 1)^2 + 5] [20(5{-1} + 1)]

f ' (-1) = 2[2(-4)^2 + 5] [20(-4)]

f ' (-1) = 2[2(16) + 5] [-80]

f ' (-1) = 2[37] [-80]

f ' (-1) = -5920

Done!

Do you advise which you particularly prefer to locate the available values of x if h(x) = 6? if so: considering the fact that h(x)=(x-a million)/(x^2-4x-12) & you prefer to locate h(x)=6, you would be able to desire to equate the two considered one of them at the same time: (x-a million)/(x^2-4x-12) = 6 subsequently equate this finished equation you will get: x - a million = 6(x^2 - 4x - 12) x - a million = 6x^2 - 24x - seventy two 6x^2 - 25x - seventy one = 0 use this equation to locate x and that i think of your available values of x could be... x = 6.10 or -a million.ninety 4 (to 3 significant figures)