Question

First derivative and sign diagram for the first derivative forthe funcation
f(x) = x^4 + 8x^3 + 18x^2 +8

Answer 1

use the power rule to find the derivative and then set the derivative equal to 0. find the zeros of the derivative funtion and then test each section to see if the derivative is positive or negative in that region...

Answer 2

for ex. if f(x) = x^2 - 3x + 2, we'd have f'(x) = 2x - 3.

setting that equal to 0 we'd have 0 = 2x-3 => x = 2/3

then our sign diagram...

so if x < 2/3 the derivative is negative and if x > 2/3 the derivative is positive.

also, the original function is decreasing from negative infinity to 2/3 and increasing from 2/3 to infinity.