Example Problem 2. Power Rule for Derivatives

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Power Rule for Derivatives. Example Problem 2 So. Now you need to find the values of x for which f (x) = x3 − 9x2 − 48x + 5 has ahorizontal tangent. If we have a horizontal tangent, that means there's going to be a slope of 0—that is, f'(x) =0. That means the derivative of f(x) is equal to 0. We will find f prime of x, differentiate the function with respect to x and set it equal to 0. So the derivative of f prime of x equals 3x squared minus 18x minus 48, and we're going toset that equal to 0. When a number is equal to 0, I have a tendency to want to factor it. Let's factor the three and the two to get minus 8 and plus 2. The equation does not have a solution when x = 8. However, when x = −2, a solutionexists. As shown in the graph above, the line has a horizontal tangent when x equals 8 and aslope of 0 when x equals negative 2.