Second Derivative Test for Rational Functions
Consider the function \(f(x)=\frac{x^2}{x-1}\). Determine the critical points of \(f(x)\) by finding \(f'(x)\) and then use the second derivative test to classify each critical point as a local maximum or local minimum. Clearly state your final answers.
Second Derivative Test and Inflection Analysis for a Cubic Function
Consider the function \(f(x) = x^3 – 6x^2 + 1\). (a) For SL: Differentiate \(f(x)\) to find the first derivative \(f'(x)\). (b) For HL: Using your result from part (a), differentiate again to obtain the second derivative \(f”(x)\) and then use the second derivative test to classify the turning points. Also, determine the x-coordinate of […]
Classifying Turning Points using Second Derivatives
Consider the cubic function \(f(x) = x^3 – 6x^2 + 9x + 15\). First, find the critical points by setting \(f'(x) = 0\). Then, use the second derivative test to classify each turning point as a local maximum or a local minimum.