Let f( x )= x 3+ ax + b with a ≠ 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).

Question

Let f( x )= x 3+ ax + b with a ≠ 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). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f'(a)=f'(b) ⇒ a=-b So f(1)=1+a+b=1

Q. Let $f (x) = x^{3} + a x + b$ 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 $f (1)$ .

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

Q. Let f(x)=x3+ax+b with a=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).

f′(a)=f′(b) ⇒a=−b So f(1)=1+a+b=1

Q. Let $f (x) = x^{3} + a x + b$ 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 $f (1)$ .

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