Patrick B. answered • 09/19/19

Math and computer tutor/teacher

f(3+h) = 2*(3+h)^2 + 10( 3+h) = (3+h) {2(3+h) + 10} = (3+h) ( 6 + 2h + 10)

= (3+h)(2h + 16)

= 2(h+8)(h+3)

= 2(h^2 + 11h + 24)

= 2h^2 + 22h + 48

f(3) = 18 + 30 = 48

the difference quotient is (2h^2 + 22h) / h = 2h + 22

as h tends to zer0, the limit is 22

the derivative is 4*x + 10 = y' = f '(x)

f'(3) = 22

The tangent line passes through (3,48) and has slope 22.

B = y - mx = 48 - 22*3 = 48 - 66 = -18

y = 22x - 18