Answer to Question #260086 in Calculus for Carmen

Question

Given that the graph of y=f(x) is symmetric about the y-axis and the gradient of the curve at any point (x, y) is 2x+b. Find the value of b.

Answer 1

If the graph is symmetric about y-axis

then it has a turning point at x=O.

Gradient at turning point =O

$2x+b= 0\quad at \>x=0$

$\implies b=0$