Question

Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the secant line that cuts the curve at x=1 and x=2

Answer 1

first find the slope of the secant line, i.e. the slope between the points \((1,1)\) and \((2,4)\)

Answer 2

you can do that pretty much in your head
right one, up 3 slope is \(m=3\)

Answer 3

then set \(2x=3\) and solve for \(x\)

Answer 4

Thanks, is 2x the derivative of f(x)?

Answer 5

yes, the derivative of \(x^2\) is \(2x\)