
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