Calculus
Consider the function f(x)=−2x2+4x+1f\(\left\)(x\(\right\))=-2x^2+4x+1 on the interval [−1,2]\(\left\[\lbrack\)-1,2\(\right\]\rbrack\). Find the critical points of ff and use the First Derivative Test to classify these points. Then, determine the absolute maximum and minimum values of ff on the specified interval (if there are any).
Consider the function f(x)=3x2x2−9f\(\left\)(x\(\right\))=\(\frac{3x^2}{x^2-9}\) on the interval [−5,5]\(\left\[\lbrack\)-5,5\(\right\]\rbrack\). Find the critical points of ff and use the First Derivative Test to classify these points. Then, determine the absolute maximum and minimum values of ff on the specified interval (if there are any).
Consider the function f(x)=−2xx+12f\(\left\)(x\(\right\))=-2x\(\sqrt{x+12}\). Determine intervals where ff is increasing and decreasing, and the intervals on which the curve is concave up and concave down.
