A curve has equation y = x 3 + 2x 2 4x + 6. a. Show

Question:

A curve has equation y = x³ + 2x² − 4x + 6.
a. Show that dy/dx = 0 when 2 and when x = -2 and when x = 2/3.

b. Find the value of d²y/dx² when x = -2 and when x = 2/3.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

ISBN: 9781108407144

1st Edition

Authors: Sue Pemberton, Julian Gilbey

See More Books

Question Posted: Mar 10, 2023 11:29 PM

See More Questions

A curve has equation y = f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P.
A curve has equation y = f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P.
A curve has equation y = 4x 3 + 3x 2 6x 1. a. Show that dy/dx = 0 when x = - 1 and when x = 0.5. b. Find the value of d 2 y/dx2 when x = - 1 and when x = 0.5.
Hernandez Company began 2010 with a $120,000 balance in retained earnings. During the year, the following events occurred: 1. The company earned net income of $80,000. 2. A material error in net...
If you save $6000 a year into a 401(k) retirement plan for 25 years and earn an average rate of interest of 6% per year, how much will you have at the end of the 25th year? (Assume the first payment...
In Figure P31.72, $\mathscr{E}_{1}=5.0 \mathrm{~V}, \mathscr{E}_{2}=5.0 \mathrm{~V}, \mathscr{E}_{3}=1.5 \mathrm{~V}$, $R_{1}=50 \Omega, R_{2}=50 \Omega$, and $R_{3}=50 \Omega$. What are (a)...
A model for chromatographic separation: a case-study problem. An important application of Taylor dispersion is in chromatography. Here pulses of a mixture of solutes are introduced into one end of a...
Vanishing Games Corporation (VGC) operates a massively multiplayer online game, charging players a monthly subscription of $ 15. At the start of January 2015, VGCs income statement accounts had zero...
What is the output? int main() { for (int i = 0; i < 3; ++i) { cout < < i; } } cout < < i; return 0;
When deciding on whether or not to crash project activities, a project manager was faced with the following information. Activities of the critical path are highlighted with an asterisk: a. Identify...
A curve has equation y = 2(x 1) 3 + 2. The normal at the point P(4, 4) and the normal at the point Q(9, 18) intersect at the point R. a. Find the coordinates of R. b. Find the area of triangle PQR.
A curve has equation and passes through the points A(2, 12) and a. Find the coordinates of the points C and D. Give your answer in exact form. b. Find the equation of the perpendicular bisector of...
What is the mean household income for females working in the Service category?
Two metallic spheres A and B are placed on nonconducting stands. Sphere A carries a positive charge, and sphere B is electrically neutral. The two spheres are connected to each other via a wire, and...
In the first quarter of the year 2015/2016, City Steels total revenues decreased by 35 per cent compared with the previous year. Adverse economic conditions caused the Groups products to decrease...
Apple Inc. is well known for developing innovative products like the iPhone, iPad and iPod. Such devices are manufactured with complex electronic components and incur substantial design and...
Most developed economies have well-developed road and highway networks. From time to time new highways are built to relieve congested cities, but by and large most developed countries are not...
Allan Stratton is a cost management consultant with over 35 years of experience who shares the benefit of his experience providing tools and resources via the internet. In one of his articles he...
Draw and name all possible isomers of pentene.
Which, if any, of the dichloroethene molecules drawn in Data Table II (3.) (4.) and (5.) are geometric isomers? A. B. C. D. cis-1,2-dichloroethene and trans-1,2-dichloroethene...
Find a 99% CI for the population variance of the concentrations? Pharmacology Suppose we want to estimate the concentration (g/mL) of a specific dose of ampicillin in the urine after various periods...
How large a sample would be needed to ensure that the length of the CI in Problem 6.30 is 0.5 g/mL assuming the sample standard deviation remains at 2.0 g/mL? Pharmacology Suppose we want to estimate...
What is the best estimate of the 1971 incidence rate from these data? Environmental Health Much discussion has taken place concerning possible health hazards from exposure to anesthetic gases. In one...
The numbers 1, 2, ..., 12 can be entered into the 12 regions of the diagram to the right so that each of the six rows of five triangles (as shown by the arrows) contains numbers that sum to the magic...
Passage - The Lobster Tale A long, long time ago in a faraway land, there was a fishing village. It had acquired a modest standard of living for its community members, and of course, fishing was the...
A wave hits the beach every 5.0 seconds, and the waves seem to be about 15m apart. a) What is the speed of these wave b) what is the frequency of the waves?

A curve has equation y = x 3 + 2x 2 4x + 6. a. Show

Question:

Step by Step Answer:

a To find the points where dydx 0 we need to differ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

Students also viewed these Mathematics questions