Question

Solve this :

9. Find the minimum and maximum values of function y = x³ - 3x² + 6. Also find the values of x at which these occure.
10. The particle's position as a function of time is given as x = 5t² - 9t + 3. Find out the maximum value of position co-ordinate ?

Answer 1

Dear Student,
$$\begin{gathered} weacnsolveonequestionatatime. \\ postotherquestioninotherthread. \\ solving9. \\ y=x^3-3x^2+6 \\ \frac{dy}{dx}=3x^2-6x=0 \\ forx=0 \\ \frac{d^{2}y}{d{x}^2}=6x-6 \\ putx=0\frac{d^{2}y}{d{x}^2}<0hencex=0isthepointofmaxima. \\ forx=2 \\ \frac{d^{2}y}{d{x}^2}=6x-6 \\ putx=2\frac{d^{2}y}{d{x}^2}>0hencex=2isthepointofminima. \\ Regrds \end{gathered}$$