Algebraically Examples of concavity: Consider the function f(x)=18x4−3x2. The first derivative would be f′(x)=12x3−6x. The second derivative would be f″(x)=32x2−6. Now, let f″(x)=0, which implies that x=−2,2,. Here, for both the values of x=2,−2, f...
Algebraically Examples of concavity: Consider the function f(x)=18x4−3x2. The first derivative would be f′(x)=12x3−6x. The second derivative would be f″(x)=32x2−6. Now, let f″(x)=0, which implies that x=−2,2,. Here, for both the values of x=2,...
To algebraically approach finding domain and range, we need to follow several steps. Let's look at them now: Steps to Finding the Domain Step 1. Set the inequality to 0 instead of y or f(x): Step 2. Factor the polynomial completely, then set each factor equal to zero to find ...