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Calculate the sum of interior angles in an octagon. Step 1: Count out how many triangles the polygon can be split into. Step 2: Multiply the number of triangles by 180° to obtain the sum of the interior angles.
These angles are congruent angles located between the parallel lines in the interior region and on opposite sides of the transversal & at different vertices. List all pairs of alternate interior angles in the diagram:
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5.3 Concavity and Inflection Points. Section 1: Determine the open intervals on which the graph s concave up or concave down. f (x) = 24 x2 + 12. f (x) = x2 + 1 x2 − 1. y = 2x − tan x π π , (− 2 ) Section 2: Find the inflection points and the open intervals of concavity.
When the second derivative is negative, the function is concave downward. And the inflection point is where it goes from concave upward to concave downward (or vice versa). Example: y = 5x 3 + 2x 2 − 3x. Let's work out the second derivative: The derivative is y' = 15x2 + 4x − 3. The second derivative is y'' = 30x + 4.
point on a graph where the concavity of the curve changes (from concave down to concave up, or vice versa) is called a point of inflection (Definition 4.14). By implication (think about what separates positive and negative numbers on a number line), if a point (c, f (c)) is a point of inflection, then f ′ ′ ( c ) = 0 .
Angles Name: _____ Instructions • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information
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Maxima and minima are also called TURNING points or STATIONARY points. Going from left to right, the gradient is DECREASING up to the point P and then it starts INCREASING again. The point P where the gradient stops decreasing and starts increasing is called an INFLECTION point.
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