Question

match each function with its derivative

Match each function with its derivative.

if you zoom you can see it

Answer 1

f(x) =

f'(x) =

Reason: The function f(x) has a minimum at 0 and maximum at 4, so the derivative of f(x) must be 0 at those point, further, the slope of f(x) increases after 0 until a point between 0 and 4, and then the slope starts decreasing. This point is called the point of inflection, which is an extreme point of f'(x), which we can see that the graph of f'(x) satisfies.

f(x) first, then f'(x)

Here we see that the function f(x) firstly decreases(that is, has negative slope, and then attains a minimum of 0 at x=3, and then increases, that is, positive slope, and all these conditions are satisfied by the bottom function, f'(x).

f(x) =

f'(x) =

This is evident by simply matching the maxima and minima point The derivative f'(x) becomes 0 at exactly the points where the function has a maxima or minima.

f(x) and f'(x)

Here also simply matching the extreme points of f(x) with the roots of f'(x) are enough.