Suppose that a point moves along some unknown curve y = f(x) in such a way that at each point (x, y) on the curve the tangent line has a slope . Find an equation for the curve, given that it passes through (1,1).

is just the the derivative of since it it is the slope of the line tangent to the curve at . To find how is defined, we'll just take the anti-derivative of .

Recall:

Solving for :

We still have to solve for . Note that the point has to be on our graph so or .

Solving for :

We can finally write or . Since , we can write it as as well.

d) the triangle is a right triangle 60 squared +144 squared= 156 squared

step-by-step explanation:

156 squared is the hypothenuse

so 156= c

except a rational number. : )