Find Where Increasing/Decreasing f(x)=x^2+4x-12

Problem

ƒ(x)=x2+4*x−12

Solution

1. Find the derivative of the function to determine the rate of change.

d(ƒ(x))/d(x)=2*x+4

2. Identify critical points by setting the derivative equal to zero and solving for x

2*x+4=0

2*x=−4

x=−2

3. Test intervals created by the critical point x=−2 to determine the sign of ƒ(x)′
   For x<−2 test x=−3 2(-3) + 4 = -2(n*e*g*a*t*i*v*e).F*o*r > -2,t*e*s(t) = 0:(0) + 4 = 4$ (positive).

4. Determine behavior based on the sign of the derivative.
   The function is decreasing where ƒ(x)′<0 and increasing where ƒ(x)′>0

Final Answer

Increasing: *(−2,∞), Decreasing: *(−∞,−2)

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