Positive Second Derivative Math

If the 2nd derivative f at a critical value is inconclusive the function may be a point of inflection.

Positive second derivative math. Anybody can ask a question anybody can answer the best answers are voted up and rise to the top home questions tags users unanswered second derivative positive but not for the minimum. Similarly a function whose second derivative is negative will be concave down also simply called concave and its tangent lines will lie above the graph of the function. A differentiable function f is increasing at a point or on an interval whenever its first derivative is positive and decreasing whenever its first derivative is negative. The only way to sketch the graph of a function at.

If the 2nd derivative f at a critical value is negative the function has a relative maximum at that critical value. Here is a possible picture of the tangent lines. Positive second derivative at x tells us that the derivative of f x is increasing at that point and graphically that the curve of the graph is concave up at that point. The second derivative measures the instantaneous rate of change of the first derivative and thus the sign of the second derivative tells us whether or not the slope of the tangent line to f is increasing or.

By taking the derivative of the derivative of a function f we arrive at the second derivative f. It only takes a minute to sign up. Conversely when the second derivative is negative the slope of the tangent lines is decreasing. The second derivative being positive implies that the graph is concave up since the slope of tangent lines must be increasing.

A function whose second derivative is positive will be concave up also referred to as convex meaning that the tangent line will lie below the graph of the function. Sign up to join this community.