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x = −b ± √(b² − 4ac) / 2a
x = −20 ± √(20² − 4(3)(-500)) / 2(3)
x = (3x + 50) (x - 10)

We start with sec^2 x + 2tanx = 0 for 0 ≤ x ≤ 2π
Note that sec^2 x = tan^2 x +1
tan ^2 x + 2tan x +1 = 0
(tan x +1)^2=0
tan x = -1
x=3π/4 or x=7π/4

F(x)= 3x³ - 7 + 5x²
i) F'(x)= 33x² + 25x
F'(x)= 9x² + 10x
ii) F''(x)= 2*9x + 10
F''(x)= 18x + 10
iii) for maximum or minimum...

In a case of integral that you want to integrate once using technique "by parts" you have to divide your integral into two functions.Working on an example, f(x)=x sinxLet g(x)=x and h'(x)= sin x...