Question

Let $f( x )= x ^{3}+ ax + b$ with $a \neq b$ and suppose the tangent lines to the graph of $f$ at $x = a\, \&\, x = b$ have the same gradient. Then find the value of $f(1)$.

Answer 1

$f'(a)=f'(b)$
$\Rightarrow a=-b$
So $f(1)=1+a+b=1$