# p1812tut04 - x showing any local maxima local minima points...

This preview shows page 1. Sign up to view the full content.

School of Mathematics and Statistics The University of Sydney PHAR1812 Calculus Tutorial 4 1. ( i ) Sketch a smooth curve whose slope is everywhere negative and increasing gradually (i.e. becoming less negative). ( ii ) Sketch a smooth curve whose second derivative is everywhere negative but whose first derivative is everywhere positive. ( iii ) Sketch a smooth curve whose first and second derivatives are everywhere negative. 2. For each of the following functions y = f ( x ) find y 0 , y 00 and sketch the curve y =
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ), showing any local maxima, local minima, points of inﬂections and asymptotes : ( i ) y = 1 1 + x 2 ( ii ) y = 2 x 3 + 3 x 2-36 x + 5 ( iii ) y = x x 2 + 1 ( iv ) y = x 10-10 x ( v ) y = x-ln x (for x > 0) ( vi ) y = x 2 + 2 ( x + 2) 2 3. Find a cubic polynomial P ( x ) with the following properties. ( i ) P (0) = 4 ( ii ) P (2) = 0 ( iii ) P has a critical point at x =-2 and P (-2) = 0. What is the nature of the critical point at x =-2?...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern