How many turning pts and what is the slope of the function f(y) = a + bx²,

Question

function: f(y) = a + bx² …

How many turning points in the function and What is the slope of the function?

Answer 1

I think you mean y=f(x)=a+bx^2.

The slope of the function we get by differentiating: f'(x)=2bx. The slope depends on x, that is, where you are on the curve. The turning point is found by putting f'(x)=0 and solving for x: 2bx=0 so x=0 and y=a, therefore (0,a) is a turning point. If b>0, f"(x)=2b which is positive and the turning point is a minimum, and there is only one. If b<0 the turning point is a maximum. The curve is a parabola.