2 at most how many turning points can the graph of fxx24x3x2

2) at most how many turning points can the graph of f(x)=x^2(4x-3)(x+2) have?

3) white an equation for a function whose graph fits the given description. the graph of f(x)= square root of xis shifted 3 units to the left and then 7 unit upward.

Solution

2) f(x)=x^2(4x-3)(x+2)

The degree of f(x) is 4 (because you have x^7 as the highest exponent).
This is one more than the number of possible turning points. In other words, you can\'t have more than *3* turning points.
General rule:
A polynomial of degree n can have at most n-1 turning points.

3) f(x) = sqrt(x + 3) + 7