Find the values?

Question

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

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Answer 1 · 2018-03-19T12:14:54

#a = -2, b = 5#

Th generic tangent line to #f(x)# at #x_0# 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#