Mohon bantuannya ya. Terimakasih

Kalkulus I tingkat perguruan tinggi.

Nomor 1
a. s = -16t² + 40t + 100
v = ds / dt = -32t + 40
t = 2 → v = -32(2) + 40 = -24 m/s

b. v' = 0
-32t + 40 = 0 → t = 1,25 s

Nomor 2
s = 4,5t² + 2t
v' = 30
9t + 2 = 30 → t ≈ 3,11 s

Nomor 3.
Lihat gambar!

Nomor 4
y = (2x - 3) / (x² + 4)²
y' = [2(x² + 4)² - (2x - 3) 2(x² + 4)(2x)] / (x² + 4)⁴
    = -2 (3x² - 6x - 4) / (x² + 4)³

Nomor 5
f(x) = [(x² + 1) / (x + 2)]³
f'(x) = 3 [(x² + 1) / (x + 2)]² {[2x (x + 2) - (x² + 1) 1] / (x + 2)²}
       = [6x (x² + 1)² (x + 2) - 3(x² + 1)³] / (x + 2)⁴
       = (x² + 1)² (6x² + 12x - 3x² - 3) / (x + 2)⁴
       = 3(x² + 1)² (x² + 4x - 1) / (x + 2)⁴
f(3) = 3(3² + 1)² (3² + 4·3 - 1) / (3 + 2)⁴
      = 9,6