CALCULUS HELP!! Suppose f (x)=4f(x)+2x and f(3)=5 Use a linear approximation to estimate f(3.011)?

rotchm

f(x) = f(a) + f '(a) Δx . This is the linear approximation, the equation of the tangent line. You are given that a=3, f(a) =5, Δx = 3.011-3 and f '(a) = 4f(a) + 2*a. Compute it all. Done!

Captain Matticus, LandPiratesInc

f'(x) = 4 * f(x) + 2x f'(3) = 4 * f(3) + 2 * 3 = 4 * 5 + 6 = 26 You need a line with a slope of 26 that passes through (3 , 5) y - 5 = 26 * (x - 3) x = 3.011 y - 5 = 26 * (3.011 - 3) y - 5 = 26 * 0.011 y - 5 = 0.286 y = 5 + 0.286 y = 5.286

Anonymous

I just know this wasn't in my Calculus class... Unless this is actually Taylor series?

david

f (x)=4f(x)+2x and f(3)=5 f' = 4f' + 2 -3f' = 2 f' = -2/3 <<< it looks like the derivative is constant meaning f(x) is linear f(3) = 5 ,,, y - 5 = (-2/3)(x - 3) ... y = (-2/3)x + 7 f(x) = (-2/3)x + 7 f(3.011) = 4.99267