lannor6586
24.01.2020 •
Mathematics
F(x)=2x^3-3x^2-12x+k
a)show that if k=30, then f(x)=0 has at least one solution
b)show that if k=30, then f(x)=0 has exactly one solution
c)find all values of k so that f(x)=0 has exactly one solution
Solved
Show answers
More tips
- B Business and Finance How to Open an Online Store? A Detailed Guide for Beginners...
- W Work and Career How to Write a Resume That Catches the Employer s Attention?...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
Answers on questions: Mathematics
- M Mathematics Betra is planning a party for her friends.the room rental cost is $50 plus an additional five dollars per person to cover food costs. veteran has saved up $100. what is...
- M Mathematics The scatterplot for a set of data points is shown, along with the line of best fit. choose the best estimate for r, the correlation coefficient. a) -1.0 b) -0.8 c) 0.8...
- M Mathematics (05.03 lc) what is the initial value of the function represented by this graph? (1 point) a coordinate grid is shown with x- and y-axes labeled from 0 to 7 at increments...
- M Mathematics It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. if the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how...
- M Mathematics Someone better me on all of these will mark the true real !...
- M Mathematics Which number is greatest or lowest 2/5 or 0.3...
- M Mathematics Pears cost $0.92 per pound and apples cost a dollar $ 1.10 per pound mr.bonilla bought 3.75 pounds of pears and 2.1 pounds of apples how much did he pay for the pears and...
- M Mathematics Chloe is sorting items at a thrift store. she finds a box of tiny blocks that has 1,344 written on the outside. she can see that each layer in the box has 64 blocks. how...
- M Mathematics What is the prime factorization of 30...
- M Mathematics What is 4 less than three sevenths of y written as an algebraic expression...
Ответ:
dy/dx = 12 - 6x - 6x^2Set this = 0
-6x^2 - 6x + 12 = 0Divide both sides by (-6)
x^2 + x - 2 = 0
(x + 2) * (x - 1) = 0
x = 1, -2
Take the second derivative: d^2y/dx^2 = -6 - 12x
This is negative at x = 1 and positive at x = -2 so we have a maximum at x = 1 and a relative minimum at x = -2
The function is increasing on (-2, 1) < Answer for (a)
f(x)= k +12x - 3x^2 - 2x^3
f(1) = k + 12 - 3 - 2 = k + 7
If you want that to be 4, then k + 7 = 4 and k = - 3 < Answer for k---(b)
I guess that I should be considering k to be -3 from here on out. You weren't specific about whether I should leave it as k or change it to -3.
So from now on the equation is: f(x)= -2x^3 -3x^2 + 12x - 3 <
f(-2) = 16 -12 -24 - 3 = 16 - 39 = - 23
So the minimum is (-2, -23) < Answer to (c)
(-∞,-2) < Answer to (d)
Ответ:
Ask me anything if you still have questions