Question

Suppose that for a function f(x) we know that
f(3)=5 and f ' (3)=7
We also 'have that g(x)=x^2*f(x)
Find the equation of the line tangent to g(x) at x=3

Answer 1

\[g'(x)=2xf(x)+x^2f'(x)\] by the product rule so
\[g'(3)=2\times 3\times f(3)+3^2f'(3)\]
plug in the numbers and get out your slope

Answer 2

My calculator keeps giving me error

Answer 3

this is not a calculator exercise

Answer 4

\[2\times 2\times5+9\times 7\] is the slope

Answer 5

6f(3)+9f'(3)

Answer 6

83

Answer 7

i meant
\[2\times 3\times 5+9\times 7\]

Answer 8

93

Answer 9

is the slope

Answer 10

yes

Answer 11

ok then what

Answer 12

the point is \((3,3^2\times 5)\)

Answer 13

better known as \((3,45)\)
last step is point - slope formula

Answer 14

ok how do you do that

Answer 15

can someone help me

Answer 16

do you know how to find the equation of a line given a point and a slope?

Answer 17

no

Answer 18

if the slope is \(m\) and the point is \((x_1,y_1)\) then the equation for the line is
\[y-y_1=m(x-x_1)\]
this is called the point - slope formula

Answer 19

what are the x and y values if you on;y have (3,45)

Answer 20

yes, that is all you need, one point \((3,45)\) and the slope \(m=93\)

Answer 21

ok so then would it be 45=93-3

Answer 22

ok lets back up a second

Answer 23

you are being asked for the equation of a line right?

Answer 24

usually it would look like \(y=mx+b\)

Answer 25

yes the tangent line at x=3

Answer 26

so your answer needs to look like \(y=mx+b\)

Answer 27

y=93x+42

Answer 28

\[y-y_1=m(x-x_1)\] is the point slope formula
replace \(m\) by \(93\), \(x_1\) by \(3\) and \(y_1\) by \(45\)

Answer 29

you get
\[y-45=93(x-3)\]

Answer 30

now you can solve this for \(y\) to make it look like \(y=mx+b\)

Answer 31

so then are the y and x 0

Answer 32

oh ok just a minute

Answer 33

y=138(x-3)

Answer 34

\[y = 93 x-234\]

Answer 35

oh ok I added the wrong thing together

Answer 36

multiply out using the distributive law, then add 45

Answer 37

ok

Answer 38

so then the y=93x-234 is the equation correct

Answer 39

i think so

Answer 40

ok thanks

Answer 41

yw