CURVE SKETCHING

Question

𝑦 = −𝑥3\3− 2𝑥2 + 5𝑥 − 2

ANSWER: 𝐶𝑃: 𝑥 = 1,−5 , IP : 𝑥 = −2, Decreasing on (−∞,−5) & (1, ∞), Increasing on (−5,1) , CU on
(−∞,−2) CD on (−2, ∞), Minimum point (−5,−106\3) , Maximum point (1,2\3)

I WANT THE STEPS PLEASE

Answer 1

y' = -x^2 - 4x + 5 = -(y+5)(y-1)
y'=0 at x = -5,1
y'<0 for x < -5 or x>1; y'>0 for -5<x<1
y" = -2x-4
y"(-5) > 0, so y is concave up (minimum)

So now you have the steps for these three. Go back and review the section where it covers 1st and2nd derivative tests.