Find the values of m and b that make the following function differentiable. the piecewise function f of x equals x squared when x is less than or equal to three or mx plus b when x is greater than three

For to be differentiable, it must be continuous, so we need to have

By its definition, . The one-sided limits are

so we require .

In order for to be differentiable at , we also need to have exist, which requires that also be continuous at . First, compute the derivatives of all pieces of :

is continuous at if

The one-side limits are

so we need to have , and moreover will be differentiable if we set .

So with , we must have .

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6