Question

Find the sum of all values of k so that the graph of y = x^2 - 2x + 7 and the graph of y = kx + 5 are tangent.

Answer 1

do you know how to find the slope of the tangent line at any point for the curve: \(y=x^2-2x+7\)?

Answer 2

no

Answer 3

have you studied calculus (specifically differentiation)?

Answer 4

I haven't

Answer 5

I was taught basic derivatives though

Answer 6

so can you find the derivative of the curve: \(y=x^2-2x+7\)?

Answer 7

I don't remember much though, but is it 2x - 2

Answer 8

that is correct

Answer 9

now the derivative represents the slope of the tangent line to the curve \(y=x^2-2x+7\) at any point.

Answer 10

so what you need to do is to imagine some point - lets call it \(x=x_1\) at which the slope of the tangent lie to this curve is equal to k.

Answer 11

also at that point, both the line \(y=kx+5\) and the curve \(y=x^2-2x+7\) have the same x and y values

Answer 12

understand so far?

Answer 13

can u start from after the derivative part again

Answer 14

so the derivative of the curve is 2x - 2
then what do u do?

Answer 15

let me sketch a graph that will help explain this