Question

helpp

Answer 1

we need to make a smooth transition from the parts

Answer 2

since they transition at x=3, what is the slope of the line at x=3?

Answer 3

another way to look at this is: what is the equation of the tangent line of x^2, at x=3

Answer 4

the slope of the line is defined by what?

Answer 5

you are taking calculus classes ...

Answer 6

how do we determine the slope of a line at a given point along a curve?

Answer 7

we take the ____________ of the function.

Answer 8

point idk

Answer 9

it starts with deriv, and ends with ative

Answer 10

the derivative of a function defines the slope of the function at any given point.

Answer 11

:)

Answer 12

hehe :)

if we know the slope of a line, and a point in that line ..... we can construct a line equation.

Answer 13

given a function f

the slope at any given point, a, is equal to f'(a)

and by using the point (a,f(a)) we can define a line as:

y = f'(a) (x-a) + f(a)

Answer 14

since f = x^2, what is f' ?

Answer 15

then:

y = 2a (x-a) + a^2

what is our value of a?

Answer 16

well, in order for the parts to meet up, then they would have to be connected when x=3 yes. so let a=3

y = 2(3) (x-3) + 3^2 gives us the tangent line equation, which is simply what the y=mx+b is calling for.

Answer 17

-18 + 9 = -9

Answer 18

its rather humbling when we forget how to add when taking a calculus class ;)