The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.

Step 1: Differentiate y with respect to x. dy/dx = 3x^2 - 6x - 9
Step 2: Equate to zero and solve. 3x^2 - 6x - 9 = 0(x - 3)(x+1) = 0x = 3, x = -1
Step 3: Substitute into original equation to find y. At x = 3, y = -13. ==>> (3, -13)At x = -1, y = 19 ==>> (-1, 19)
Step 4: Find the second derivatived^2y/dx^2 = 6x - 6
Step 5: Determine the nature of the stationery pointsAt x = 3, d^2y/dx^2 = 12Therefore, (3, -13) = MINIMUMAt x = -1, d^2y/dx^2 = -12Therefore, (-1, 19) = MAXIMUM

DA
Answered by Daniel A. Maths tutor

4166 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What does a 95% confidence interval reflect?


Find the positive value of x such that log (x) 64 = 2


What is an easy way to remember how sin(x) and cos(x) are differentiated and integrated?


Why, how and when do we use partial fractions and polynomial long division?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences