Question

Find an equation for the tangent line to the specified graph at the point given.
the graph of y=x^2 at (4, 16).

I need detailed explaination because I am just not following. Thanks

Answer 1

your graph is a parabola that runs through the origin, at the point (4,16) we want to find the equation of the tangent line y=mx+b

Answer 2

because the line is tangent to our graph the slope of the tangent line and the slope at the point on our graph are equal

Answer 3

take the derivative of the graph and plug in the value of x to find the slope at that point

Answer 4

y'=2x evaluated at 4 = 8

Answer 5

\[m=\frac{y1-y}{x1-x}=\frac{16-y}{4-x}\]

Answer 6

\[\frac{16-y}{4-x}=8\]

Answer 7

16-y=8(4-x)

Answer 8

how is that 8?

Answer 9

16-32+8x=y and your equation is y=8x-16

Answer 10

m is equal to slope and we no slope is y'=2(4)=8 so we can set them equal to each other

Answer 11

i dont under stand the inverse. it goes from y = x^2 to just 2x?

Answer 12

thats the derivative of the function power rule

Answer 13

d/dx x^n = nx^n-1

Answer 14

oh yeah you bring it out front. ok sorry.

Answer 15

its all good its a tricky question and tough to learn from a message board