• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 20
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Find the polynomial f(t) of degree 3 such that f(1)=(1),f(2)=5,f'(1)=2,and f'(2)=9 , where f'(t) is the derivative of f(t) . Graph this polynomial.

The graphical representation of the cubic polynomial f'(t)=-5+13t-10t2+3t2 is,

See the step by step solution

Step by Step Solution

Step 1: Consider the points and form the equations

The equation is, ft=a+bt+ct2+dt3

The derivative of the equation is, f't=b+2ct+3dt2

Substitute the points in the above equation to form the equations.

localid="1659349415086" (1,1): f(1)=a+b(1)+c(1)2+d(1)3 =1a+b+c+d=1 ....(1) (2,5): f(2)=a+b(2)+c(2)2+d(2)3 =-1a+2b+4c+8d=5 ......(2) (1,2): f'(1)=b(3)+2(c)+3d(3)2 =2b+2c+3d=2 .......(3) (2,9): f'(2)=b(3)+2c(3)2+3d32 =9b+4c+12d=9 .............(4)

Step 2: Consider the matrix

Re-write the equations in terms of a matrix.


The matrix form is,


Step 3: Solve the matrix

Consider the matrix.


Using row Echelon form to reduce the matrix.

111111248501232014129=111110137400-1-4-200013 =1000-50100130010-1000013

The values are, a=-5,b=13,c=-10,d=3

Therefore, the polynomial is,

f(t)=a+bt+ct2+dt3 =-5+13t-10t2+3t3

Step 4: Sketch the graph

The graphical representation of f(t)=-5+13t-10t2+3t3 is, ss

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.