Home > Calculus > Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

What is the derivative graph of a parabola?

Answer 1

The formula for a parabola is #y = ax^2 + bx + c#, where #a, b and c# are numbers. If you take the derivative of this: #d/dx (ax^2 + bx + c) = 2ax + b# So the derivative function is #y = 2ax+b# If you grave this, you will always get a line, since this is a function of the first order.

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Answer 2

Paisley Johnson

The derivative graph of a parabola is a straight line. If the original parabola opens upwards, the derivative graph is a line that slopes upward from left to right. If the original parabola opens downwards, the derivative graph is a line that slopes downward from left to right.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.