Question

Find an equation of the tangent line to the graph of "f" at the given point.

f(x)=x²+3, (1,4)

Answer 1

do you know what the derivative of
\[f(x)=x^2+3\] is?

Answer 2

No

Answer 3

do you know the power rule or the constant rule?

Answer 4

Yes, I do.

Answer 5

Then use them to find the derivative.

Answer 6

Power Rule
\[(x^n)'=nx^{n-1} \]
Constant Rule (C is a constant)
\[(C)'=0\]

Answer 7

\[f'(x)=(x^2)'+(3)'=?\]

Answer 8

2x?

Answer 9

yep

Answer 10

f'(1) will be the slope
remember f'(x)=2x
so what is f'(1)=?

Answer 11

2

Answer 12

so we know this about the tangent line y=2x+b
so we need one more thing, the y-intercept

Answer 13

You know a point on this line (1,4)
Plug it in to find b, the y-intercept.

Answer 14

\[4=2(1)+b\]
I replaced x with 1 and y with 4.

Answer 15

find b

Answer 16

b=2

Answer 17

so the tangent line is y=mx+b
where m=2 and b=2
y=2x+2

Answer 18

alright, thank you

Answer 19

A plot is attached.