For the following exercises, determine intervals where f is increasing or decreasing, local minima and maxima of f , intervals where f is concave up and concave down, and the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. 231. [T] f ( x ) = sin ( π x ) − cos ( π x ) over x = [-1, 1]
For the following exercises, determine intervals where f is increasing or decreasing, local minima and maxima of f , intervals where f is concave up and concave down, and the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. 231. [T] f ( x ) = sin ( π x ) − cos ( π x ) over x = [-1, 1]
intervals where f is concave up and concave down, and
the inflection points of f. Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator.
231. [T]
f
(
x
)
=
sin
(
π
x
)
−
cos
(
π
x
)
over x = [-1, 1]
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY