Q.13 - Calculus

Question

If a function f has four critical points, how many calculations after finding derivatives are required in order to apply the first-derivative test? The second-derivative test? 

Step-by-Step Solution

Answer

Five calculations will be needed after finding the first derivatives in order to apply the first derivative test. 

Three calculations for each point of four points will be needed after finding the second derivatives in order to apply the second derivative test.

Step 1. Given information.

a function f has four critical points.

Step 2. Explanation.

Consider function f has critical points $x=c_1,c_2,c_3, \& c_4$

Then interval will be $\left(-\infty ,c_1\right),\left(c_1,c_2\right),\left(c_2,c_3\right),\left(c_3,c_4\right), \& \left(c_4,\infty \right).$

There are five intervals so five calculations will be needed after finding the first derivatives in order to apply the first derivative test.

three calculations for each point of four points will be needed after finding the second derivatives in order to apply the second derivative test because we will need to find whether the points give local minima or maxima or nither.