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Negative of a convex function
mathsathome.com
- A function that has an increasing first derivative bends upwards and is known as a convex function. On the other hand, a function, that has a decreasing first derivative is known as a concave function and bends downwards. We also describe a concave function as a negative of a convex function.
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A cubic function is concave (left half) when its first derivative (red) is monotonically decreasing i.e. its second derivative (orange) is negative, and convex (right half) when its first derivative is monotonically increasing i.e. its second derivative is positive
Aug 24, 2022 · My question is, if we take a concave function like the picture below, and take the negative of it, will it become convex? Since the appearance will be U-shaped just like a convex function. I understand that the inequality for concave function still holds if we negate the function.
A function f is concave if the 2nd derivative f’’ is negative (f’’ < 0). Graphically, a concave function opens downward, and water poured onto the curve would roll off. A function f is convex if f’’ is positive (f’’ > 0).
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Taking the second derivative actually tells us if the slope continually increases or decreases. When the second derivative is positive, the function is concave upward. When the second derivative is negative, the function is concave downward.
Convex curves curve downwards and concave curves curve upwards. That doesn’t sound particularly mathematical, though… When f''(x) \textcolor{purple}{> 0}, we have a portion of the graph where the gradient is increasing, so the graph is convex at this section.
A function that has an increasing first derivative bends upwards and is known as a convex function. On the other hand, a function, that has a decreasing first derivative is known as a concave function and bends downwards. We also describe a concave function as a negative of a convex function.
Dec 21, 2020 · Interval 2, (− 1, 0): For any number c in this interval, the term 2c in the numerator will be negative, the term (c2 + 3) in the numerator will be positive, and the term (c2 − 1)3 in the denominator will be negative. Thus f ″ (c)> 0 and f is concave up on this interval.
