Find the values?

Find the values of a and b so that the function f(x) = x^2x2 + axax + b has the tangent
line 2y − 4x = 2 at the point (2, 5).

1 Answer
Mar 19, 2018

a = -2, b = 5a=2,b=5

Explanation:

Th generic tangent line to f(x)f(x) at x_0x0 is

y = f(x_0) + f'(x_0)(x-x_0)

here

f(x_0) = x_0^2+ax_0 + b and
f'(x_0) = 2x_0+a then comparing

y = x_0^2+ax_0 + b+(2x_0+a)(x-x_0) at x_0 = 2

y = 4+2a+b+(4+a)(x-2) = b-4+(a+4)xequiv y =2x+1

so

{(b-4=1),(a+4=2):}

and solving

a = -2, b = 5