Given: ๐‘“(๐‘ฅ) = ๐‘Ž๐‘ฅ^3 + ๐‘๐‘ฅ^2 โˆ’ 3 and ๐‘“"(โˆ’2) = 0. If it is further given that the point (โˆ’3; 6) lies on the graph of ๐‘“. Show that ๐‘Ž = 1/3 and ๐‘ = 2.

We start off by finding the first derivative of equation f(x) = ax3 + bx2 - 3: f'(x) = 3ax2 + 2bx. We now take the second derivative of equation f, because we have been told that f"(-2) = 0: f"(x) = 6ax + 2b (1). We know that with an x value of -2, equation (1) is equal to 0: f"(-2) = 6a(-2) + 2b = 0-12a +2b = 0 (2). This equation will be used later to find the final answer. We also know that the pointย (โˆ’3; 6) lies on the graph of ๐‘“. Therefore, for an x value of -3, f(x) equals 6: f(-3) = a(-3)2 + b(-3)2 - 3 = 6-27a + 9b = 9 (3). We then solve equations (2) and (3) simultaneously, as we have two unknowns and two equations, and reach the following answer: a = 1/3 ; b = 2. This question would be worth a total of 6 points.

Answered by Neil L. โ€ข Maths tutor

2376 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers โ–ธ

Factorise 3x^3y^2-6x^2y+9xy


The equation of line 1 is: 3y-5x+3=0. The equation of line 2 is : y= 5x/3+9. Check whether the 2 lines intercept.


1. Find the value of the missing edge to 2 decimal places 2. Find the angle ฮธ to 2 decimal places


Draw the line X+Y=3 on the graph from x = -3 to x = 3


We're here to help

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

ยฉ MyTutorWeb Ltd 2013โ€“2025

Terms & Conditions|Privacy Policy
Cookie Preferences