Question

Let f(x)=x^2+x+13. What is the value of x for which the tangent line to the graph of y=f(x) is parallel to the x -axis?

Answer 1

The curve f(x) = x² + x + 13

y = x² + x + 13

Differentiate each side with respect to x .

y ' = 2x + 1

Tangent line is parallel to x axis, slope of x axis = 0

So, slope of the tangent line = y ' = 0

2x + 1 = 0

2x = -1

x = -1/2